{"title": "Predictive Sequence Learning in Recurrent Neocortical Circuits", "book": "Advances in Neural Information Processing Systems", "page_first": 164, "page_last": 170, "abstract": null, "full_text": "Predictive Sequence Learning in Recurrent \n\nNeocortical Circuits* \n\nR.P.N.Rao \n\nComputational Neurobiology Lab and \n\nSloan Center for Theoretical Neurobiology \n\nThe Salk Institute, La Jolla, CA 92037 \n\nrao@salk.edu \n\nT. J. Sejnowski \n\nComputational Neurobiology Lab and \n\nHoward Hughes Medical Institute \n\nThe Salk Institute, La Jolla, CA 92037 \n\nterry@salk.edu \n\nAbstract \n\nNeocortical circuits are dominated by massive excitatory feedback:  more \nthan eighty percent of the synapses made by excitatory cortical neurons \nare onto other excitatory cortical neurons.  Why is there such massive re(cid:173)\ncurrent excitation in the neocortex and what is its role in cortical compu(cid:173)\ntation? Recent neurophysiological experiments have shown that the plas(cid:173)\nticity of recurrent neocortical synapses is governed by a temporally asym(cid:173)\nmetric Hebbian learning rule.  We  describe how such a rule may  allow \nthe cortex to modify recurrent synapses for prediction of input sequences. \nThe goal is to predict the next cortical input from the recent past based on \nprevious experience of similar input sequences. We show that a temporal \ndifference learning rule for prediction used in conjunction with dendritic \nback-propagating action potentials reproduces the temporally asymmet(cid:173)\nric Hebbian plasticity observed physiologically. Biophysical simulations \ndemonstrate that a network of cortical neurons can learn to predict mov(cid:173)\ning stimuli and develop direction selective responses as a consequence of \nlearning. The space-time response properties of model neurons are shown \nto be similar to those of direction selective cells in alert monkey VI. \n\n1  INTRODUCTION \n\nThe neocortex is characterized by an extensive system of recurrent excitatory connections \nbetween neurons in a given area.  The precise computational function of this  massive re(cid:173)\ncurrent excitation remains unknown.  Previous modeling studies have suggested a role for \nexcitatory feedback in amplifying feedforward inputs [1].  Recently, however, it has been \nshown that recurrent excitatory connections between cortical neurons are modified accord(cid:173)\ning to a temporally asymmetric Hebbian learning rule:  synapses that are activated slightly \nbefore the cell fires are strengthened whereas those that are activated slightly after are weak(cid:173)\nened [2, 3].  Information regarding the postsynaptic activity of the cell is conveyed back to \nthe dendritic locations of synapses by back-propagating action potentials from the soma. \n\nIn this paper, we explore the hypothesis that recurrent excitation subserves the function of \nprediction and generation of temporal sequences in neocortical circuits [4, 5, 6].  We show \n\n\"This research was supported by the Sloan Foundation and Howard Hughes Medical Institute. \n\n\fPredictive Sequence Learning in Recurrent Neocortical Circuits \n\n165 \n\nthat a temporal difference based learning rule for prediction applied to backpropagating ac(cid:173)\ntion potentials reproduces the experimentally observed phenomenon of asymmetric Heb(cid:173)\nbian plasticity. We then show that such a learning mechanism can be used to learn temporal \nsequences and the property of direction selectivity emerges as a consequence of learning to \npredict moving stimuli.  Space-time response plots of model neurons are shown to be similar \nto those of direction selective cells in alert macaque VI. \n\n2  TEMPORALLY ASYMMETRIC HEBBIAN PLASTICITY AND \n\nTEMPORAL DIFFERENCE LEARNING \n\nTo  accurately  predict input sequences,  the  recurrent excitatory connections in a  network \nneed to be adjusted such that the appropriate set of neurons are activated at each time step. \nThis can be  achieved by  using  a \"temporal-difference\" (TD) learning rule [5,  7].  In this \nparadigm of synaptic plasticity, an activated synapse is strengthened or weakened based on \nwhether the difference between two temporally-separated predictions is  positive or nega(cid:173)\ntive.  This minimizes the errors in prediction by ensuring that the prediction generated by \nthe neuron after synaptic modification is closer to the desired value than before (see [7]  for \nmore details). \n\nIn order to ascertain whether temporally-asymmetric Hebbian learning in cortical neurons \ncan be interpreted as a fonn of temporal-difference learning, we used a two-compartment \nmodel of a cortical neuron consisting of a dendrite and a soma-axon compartment. The com(cid:173)\npartmental model  was  based on a previous study  that demonstrated the ability  of such a \nmodel  to  reproduce a range of cortical response properties [8] .  The presence of voItage(cid:173)\nactivated  sodium channels in  the dendrite allowed  back-propagation of action  potentials \nfrom the soma into the dendrite.  To study plasticity, excitatory postsynaptic potentials (EP(cid:173)\nSPs) were elicited at different time delays with respect to postsynaptic spiking by presynap(cid:173)\ntic activation of a single excitatory synapse located on the dendrite.  Synaptic currents were \ncalculated using  a kinetic model of synaptic transmission with model parameters fitted  to \nwhole-cell recorded AMPA currents (see [9] for more details).  Synaptic plasticity was sim(cid:173)\nulated by incrementing or decrementing the value for maximal synaptic conductance by an \namount proportional to the temporal-difference in the postsynaptic membrane potential at \ntime instants t + ~t and t - ~t for presynaptic activation at time t.  The delay parameter \n~t was set to 5 ms to yield results consistent with previous physiological experiments [2]. \nPresynaptic input to  the model neuron was  paired  with postsynaptic spiking by  injecting \na depolarizing current pulse (10 ms,  200 pA) into the soma.  Changes in synaptic efficacy \nwere monitored by applying a test stimulus before and after pairing, and recording the EPSP \nevoked by the test stimulus. \n\nFigure I A shows the results of pairings in which the postsynaptic spike was triggered 5 ms \nafter and 5 ms before the onset of the EPSP respectively.  While the peak EPSP amplitude \nwas increased 58.5% in the former case, it was decreased 49.4% in the latter case, qualita(cid:173)\ntively similar to experimental observations [2]. The critical window for synaptic modifica(cid:173)\ntions in the model depends on the parameter ~t as well as the shape ofthe back-propagating \naction potential.  This window of plasticity was examined by varying the time interval be(cid:173)\ntween presynaptic stimulation and postsynaptic spiking (with ~t = 5 ms).  As  shown in \nFigure IB, changes in synaptic efficacy exhibited a highly asymmetric dependence on spike \ntiming similar to physiological data [2].  Potentiation was observed for EPSPs that occurred \nbetween I and 12 ms before the postsynaptic spike, with maximal potentiation at 6 ms.  Max(cid:173)\nimal depression was observed for EPSPs occurring 6 ms after the peak of the postsynaptic \nspike and this depression gradually decreased, approaching zero for delays greater than  10 \nms.  As in rat neocortical neurons, Xenopus tectal neurons, and cultured hippocampal neu(cid:173)\nrons (see [2]), a narrow transition zone (roughly 3 ms in the model) separated the potentia(cid:173)\ntion and depression windows. \n\n\f166 \n\nR.  P.  N.  Rao and T.  J.  Sejnowski \n\n:~  - - - - r - - - -\n\n, \n\n____   100 \n\nA \nbefore \n-----\" \n\npairing \n\n: I . \n\n-\n\nI~< \n\n~ , \n15m. \n\nbefote \n\n\"-! i  .... -\"'.J \n\nIS  ~  B \n\n150 \n\n~ ~ \nISma \n\n~ \n]-\n\n~ i  i OO~ _ _ _  J \n\n.5  -50 \n\n_ __ Jl__ _ ___ \n\nafler :  \n\n--'1 \n\n, \n:~ I>m.\n\nIS \n---.J ~ \nIS \n\nI~  ~ \nc: \nCU  -100 \n_____ - - - - - - r - - - - U \n.c \n\n~ < \nISms \n\n: \nI \n, \n\nafter \n\nI \n\nI \n\u2022 \nSI \n\nI \n& \nS2 \n\n-40 \n\no \n\n-20 \nTime of Synaptic Input (ms) \n\n20 \n\n40 \n\nFigure l:  Synaptic Plasticity in a Model Neocortical Neuron.  (A) (Left Panel) EPSP in the model \nneuron evoked by a presynaptic spike (S 1) at an excitatory synapse (\"before\").  Pairing this presynap(cid:173)\ntic spike with postsynaptic spiking after a 5 ms delay (\"pairing\") induces long-term potentiation (\"af(cid:173)\nter\").  (Right Panel) If presynaptic stimulation (S2) occurs 5 ms after postsynaptic firing. the synapse \nis weakened resulting in a corresponding decrease in peak EPSP amplitude. (B) Critical window for \nsynaptic plasticity obtained by varying the delay between pre- and postsynaptic spiking (negative de(cid:173)\nlays refer to presynaptic before postsynaptic spiking). \n\n3  RESULTS \n\n3.1  Learning Sequences using Temporally Asymmetric Hebbian Plasticity \n\nTo see how a network of model neurons can learn sequences using the learning mechanism \ndescribed above, consider the simplest case of two excitatory neurons N 1 and N2 connected \nto each other, receiving inputs from two separate input neurons 11  and 12 (Figure 2A). Sup(cid:173)\npose input neuron 11  fires  before input neuron 12,  causing neuron Nl to  fire  (Figure 2B). \nThe spike from Nl results in a sub-threshold EPSP in N2 due to the synapse S2.  If input \narrives from 12 any time between land 12 ms after this EPSP and the temporal summation \nof these two EPSPs causes N2 to fire, the synapse S2 will be strengthened.  The synapse S l, \non the other hand, will be weakened because the EPSP due to N2 arrives a few milliseconds \nafter Nl  has fired. Thus, on a subsequent trial, when input 11  causes neuron Nl to fire,  Nl \nin turn causes N2 to fire several milliseconds before input 12 occurs due to the potentiation \nof the recurrent synapse S2 in previous trial(s) (Figure 2C). Input neuron 12 can thus be in(cid:173)\nhibited by  the predictive feedback from  N2 just before the occurrence of imminent input \nactivity (marked by an asterisk in Figure 2C). This inhibition prevents input 12 from further \nexciting N2.  Similarly,  a positive feedback loop between neurons Nl  and N2 is avoided \nbecause the synapse S 1 was weakened in previous trial(s)  (see arrows in Figures 2B  and \n2C). Figure 2D depicts the process of potentiation and depression of the two synapses as a \nfunction of the number of exposures to the 11-12 input sequence.  The decrease in latency \nof the predictive spike elicited in N2 with respect to the timing of input 12 is shown in Fig(cid:173)\nure 2E. Notice that before learning, the spike occurs 3.2 ms after the occurrence of the input \nwhereas after learning, it occurs 7.7 ms before the input. \n\n3.2  Emergence of Direction Selectivity \n\nIn a second set of simulations, we used a network of recurrently connected excitatory neu(cid:173)\nrons as shown in Figure 3A receiving retinotopic sensory input consisting of moving pulses \nof excitation (8  ms pulse of excitation at each neuron) in the rightward and leftward direc(cid:173)\ntions.  The task of the network was to predict the sensory input by learning appropriate recur(cid:173)\nrent connections such that a given neuron in the network starts firing  several milliseconds \nbefore the arrival of its input pulse of excitation. The network was comprised of two paral(cid:173)\nlel chains of neurons with mutual inhibition (dark arrows) between corresponding pairs of \nneurons along the two chains.  The network was initialized such that within a chain, a given \n\n\fPredictive Sequence Learning in Recurrent Neocortical Circuits \n\n167 \n\nA \n\nB \n\n11 \n\nSI \n\nS2 \n\nExcitato ry Neuron N2 \n\nInput Neuron 11  r. \n\nInput Neuron 12 \n\nInput  I \n\nInput 2 \n\nBefore  Learning \n\nC \n\nAfter Learning \n\nNI \n\nII \n\nD \n\n0 .03 \n\no \no \n\nE \n\n4 \n\n6 \nSynapse S2  66 \n\n\u00b00000000000 0 000000 \n\n10 \n30 \nTime (number of trials) \n\n20 \n\n40 \n\n.. . . .  .. .. \n\nN2  L \n\n~~ < \n\n15  illS \n\n\u2022 \u2022 \u2022 \u2022 \n\nV) \n\n2 \n\n\u00a7 \n~ \n~  0\u00b7 \u00b7 \n\n.. .::  -2 \n.~ \n\"E \n... 0 \nd::  -4 \nu \" ~  -8 \n\n;>,  -6 \n\nj \n\n~ ~ \n15  illS \n\n~j~  I ~ \n12  1  12 \n\n~ \n\n0 \n\n10 \n\n30 \nTime (number of trials) \n\n20 \n\n... .... \n\n40 \n\nFigure 2:  Learning to Predict using Temporally Asymmetric Hebbian Learning.  (A)  Network \nof two model neurons Nl and N2 recurrently connected via excitatory synapses SI and S2, with input \nneurons 11  and 12. Nl and N2 inhibit the input neurons via inhibitory interneurons (darkened circles). \n(B)  Network activity elicited by  the sequence 11  followed  by 12.  (C) Network activity for  the same \nsequence after 40 trials of learning.  Due to  strengthening of recurrent synapse S2.  recurrent excita(cid:173)\ntion from  Nl  now causes N2 to  fire  several ms before the expected arrival of input 12 (dashed line). \nallowing  it to inhibit 12  (asterisk).  Synapse  SI  has  been  weakened. preventing  re-excitation of Nl \n(downward arrows show decrease in EPSP). (D) Potentiation and depression of synapses S 1 and S2 \nrespectively during the course of learning. Synaptic strength was defined as maximal synaptic conduc(cid:173)\ntance in the kinetic model of synaptic transmission [9].  (E) Latency of predictive spike in N2 during \nthe course of learning measured with respect to the time of input spike in 12 (dotted line). \n\nexcitatory neuron received both excitation and inhibition from its predecessors and succes(cid:173)\nsors (Figure 3B). Excitatory and inhibitory synaptic currents were calculated using kinetic \nmodels of synaptic transmission based on properties of AMPA and GABAA  receptors as \ndetermined from whole-cell recordings [9].  Maximum conductances for all synapses were \ninitialized to small positive values (dotted lines in Figure 3C) with a  slight asymmetry in \nthe recurrent excitatory connections for breaking symmetry between the two chains. \n\nThe network was exposed alternately to leftward and rightward moving stimuli for a total of \n100 trials.  The excitatory connections (labeled 'EXC' in Figure 3B) were modified accord(cid:173)\ning to the asymmetric Hebbian learning rule in Figure IB while the excitatory connections \nonto the inhibitory interneuron (labeled 'INH') were modified according to an asymmetric \nanti-Hebbian learning rule that reversed the polarity of the rule in Figure lB . The synaptic \nconductances learned by two neurons (marked NI  and N2 in Figure 3A) located at corre(cid:173)\nsponding positions in the two chains after 100 trials of exposure to the moving stimuli are \nshown in  Figure 3C (solid line).  Initially,  for rightward motion,  the slight  asymmetry in \n\n\f168 \n\nA \n\nR.  P N.  Rao and T.  J.  Sejnowski \n\nB \nl \n\n-4 \n\nRecurrent Excitatory Connections (EXC) \n\n-3 \n\n-2 \n\n-I \n\n() \n\n2 \n\n4 \n\nRecurrent Inhibitory Connections (INH) \n\n- - - Input Stimulus (Rightward)f----\n\n-4 \n\n-3 \n\n-2 \n\n-l \n\n() \n\n2 \n\n4 \n\nc \n\nNeuron NI \n\nEXC \n\nNeuron N2 \n\nD \n\nNeuron NI \n\n(Right-Selective) \n\nNeuron N2 \n\n(Left-Selective) \n\nI11II111111  ~~ \n\n~~ \n\nRightward \nMotion \n\nLLflward \n\n-.PJUL. Motion \n\nI11I I111111 \n\nSynapse Number \n\nSynapse  Number \n\nFigure 3:  Direction Selectivity in the Model.  (A)  A model  network consisting of two  chains  of \nrecurrently connected neurons receiving retinotopic inputs_  A given neuron receives recurrent excita(cid:173)\n-tiorrand recurrent inhibition (white-headed arrows) as well as inhibition (dark-headed arrows) from its \ncounterpart in the other chain_  (B) Recurrent connections to a given neuron (labeled  '0') arise from \n4 preceding  and  4 succeeding  neurons  in  its chain.  Inhibition  at  a given neuron  is  mediated  via a \nGAB Aergic interneuron (darkened circle).  (C) Synaptic strength of recurrent excitatory (EXC) and in(cid:173)\nhibitory (IN H) connections to neurons Nt and N2 before (dotted lines) and after learning (solid lines). \nSynapses were adapted during  100 trials  of exposure to alternating leftward and rightward  moving \nstimuli.  (D) Responses of neurons Nt and N2 to rightward and leftward moving stimuli_  As  a result \nof learning, neuron N 1 has become selective for rightward motion (as have other neurons in the same \nchain)  while  neuron  N2  has  become selective for leftward motion_  In  the preferred direction,  each \nneuron starts firing several milliseconds before the actual input arrives at its soma (marked by an as(cid:173)\nterisk) due to recurrent excitation from preceding neurons_  The dark  triangle represents the start of \ninput stimulation in the network. \n\nthe initial excitatory connections of neuron Nl allows it to fire slightly earlier than neuron \nN2 thereby inhibiting neuron N2.  Additionally, since the EPSPs from neurons lying on the \nleft of Nt  occur before Nl fires,  the excitatory synapses from these neurons are strength(cid:173)\nened while the excitatory synapses from these same neurons to the inhibitory interneuron are \nweakened according to the two learning rules mentioned above.  On the other hand, the ex(cid:173)\ncitatory synapses from neurons lying on the right side ofNl are weakened while inhibitory \nconnections are strengthened since the EPSPs due to these connections occur after Nl has \nfired.  The synapses on neuron N2 and  its  associated  interneuron remain unaltered since \nthere is no postsynaptic firing (due to inhibition by Nl) and hence no back-propagating ac(cid:173)\ntion potentials in the dendrite.  As shown in Figure 3C, after  lOO trials, the excitatory and \ninhibitory connections to neuron Nl exhibit a marked asymmetry, with excitation originat(cid:173)\ning from neurons on the left and inhibition from neurons on the right.  Neuron N2 exhibits \nthe opposite pattern of connectivity. As expected, neuron Nl was found to be selective for \nrightward motion while neuron N2 was selective for leftward motion (Figure 3D). More(cid:173)\nover, when stimulus motion is in the preferred direction, each neuron starts firing  several \nmilliseconds before the time of arrival of the input stimulus at its soma (marked by an as(cid:173)\nterisk) due to recurrent excitation from preceding neurons.  Conversely, motion in the non(cid:173)\npreferred direction triggers recurrent inhibition from preceding neurons as well as inhibition \n\n\fPredictive Sequence Learning in Recurrent Neocortical Circuits \n\n169 \n\nMonkey Data \n\n...\u2022 ' \n\n5~ __ ~'~\u00b7~\u00b7u'~'~\"_'~~ ____ ~'= _____ \u00b7_\u00b7 \n\n.. \n. . \n--.... ~ \n~ \u2022... - ... \np.!i!  , .. '. . \n_~_~_~~ \n............ n. \ng j, ~~.~ : \u00b7jHT!: %\u00a7\u00a7: \n~ r ~.; \"::n:; ;,::= :: : :: \n;\n\n~ \n~3- \u2022 \n\ntH1\u00b7 \n\n'Cd  . . . .  - , . .  \nr f t r_ -4  \n\n.\u2022  :dc' \n\nn ... \n\n. . . . .  \n\nem  6ft.  1'b'1 \n\n'  , \n\u2022 \u2022   0..  - \" , . ,  \n\nModel \n\n. . . \n\n. \n\n\u2022 \u2022  \n\nIL \u2022 \u2022  \n\nsO'  rtn \nh \n+ \nrow \n- +.+' \nd  h,  d  \" 'd  \n=f-\n\nn  h \n\n'ft. \n. . . . . . . . .  'h,tr  te-\n\n'hz  \u2022 \u2022  d  + -\n\n\u2022 \u2022  _. \n\n~ \n;::I:; \n\n....... -----\n\nstimulus \n\nQ) \nQ. en  1 \n\n~ \n~ \n\nC\\I  6 \n\nStimylus \n\n\u2022 \n\n\u2022 \n.  _. \n\nhzc+  no \n\n\u2022  ....... \n_\u00b7h.e  ~I~ ________  ~ \n\nr - '  1\u00b7~  N  0 \n\nlime (rLonds) \n\n50 \n\ntime (ms) \n\n100 \n\nFigure 4:  Comparison of Monkey and Model Space-Time Response Plots.  (Left)  Sequence of \nPSTHs obtained by flashing optimally oriented bars at 20 positions across the 50 -wide receptive field \n(RF) of a complex cell in alert monkey V 1 (from [11)).  The cell's preferred direction is from the part \nof the RF represented at the bottom towards the top.  Flash duration = 56  ms;  inter-stimulus delay = \n100 ms; 75 stimulus presentations.  (Right) PSTHs obtained from a model neuron after stimulating the \nchain of neurons at 20 positions to the left and right side of the given neuron.  Lower PSTHs represent \nstimulations on the preferred side while upper PSTHs represent stimulations on the null side. \n\nfrom  the active neuron in the corresponding position in the other chain.  Thus, the learned \npattern of connectivity allows the direction selective neurons comprising the two chains in \nthe network to conjointly code for and predict the moving input stimulus in each direction. \nThe average firing rate of neurons in the network for the preferred direction was 75.7 Hz, \nwhich is  in the range of cortical firing  rates for moving bar stimuli.  Assuming a 200 /-tm \nseparation between excitatory model neurons in each chain and utilizing known values for \nthe cortical magnification factor in  monkey striate  cortex, one can estimate the  preferred \nstimulus velocity of model neurons to be 3.1 \u00b0 Is in the fovea and 27.9\u00b0 Is in the periphery (at \nan eccentricity of 8\u00b0).  Both of these values fall  within the range of monkey striate cortical \nvelocity preferences [11]. \n\nThe model predicts that the neuroanatomical connections for a direction selective neuron \nshould exhibit a pattern of asymmetrical excitation and inhibition similar to  Figure 3C. A \nrecent study of direction selective cells in awake monkey VI found excitation on the pre(cid:173)\nferred side of the receptive field and inhibition on the null side consistent with the pattern of \nconnections learned by the model [11]. For comparison with this experimental data, sponta(cid:173)\nneous background activity in the model was generated by incorporating Poisson-distributed \nrandom excitatory and inhibitory alpha synapses on the dendrite of each model neuron. Post \nstimulus time histograms (PSTHs) and space-time response plots were obtained by flashing \noptimally oriented bar stimuli at random positions in the cell's activating region. As shown \nin Figure 4, there is good qualitative agreement between the response plot for a complex cell \nand that for the model.  Both space-time plots show a progressive shortening of response \nonset time and an increase in response transiency going in  the preferred direction:  in the \nmodel, this is due to recurrent excitation from progressively closer cells on the preferred \nside.  Firing is reduced to below background rates 40-60 ms after stimulus onset in the up(cid:173)\nper part of the plots:  in the model, this is due to recurrent inhibition from cells on the null \nside.  The response transiency and shortening of response time course appears as  a slant in \nthe space-time maps, which can be related to the neuron's velocity sensitivity [11]. \n\n\f170 \n\nR. P.  N.  Rao and T.  J.  Sejnowski \n\n4  CONCLUSIONS \nOur results show that a network of recurrently connected neurons endowed with a temporal(cid:173)\ndifference based asymmetric Hebbian learning mechanism can learn a predictive model of \nits  spatiotemporal inputs.  When  exposed to  moving stimuli, neurons in a simulated net(cid:173)\nwork learned to fire  several milliseconds before the expected arrival of an input stimulus \nand developed direction selectivity as a consequence of learning. The model predicts that a \ndirection selective neuron should start responding several milliseconds before the preferred \nstimulus enters its retinal input dendritic field  (such predictive neural activity has recently \nbeen reported in retinal ganglion cells [10)).  Temporally asymmetric Hebbian learning has \npreviously been suggested as a possible mechanism for sequence learning in the hippocam(cid:173)\npus  [4]  and as  an  explanation for the asymmetric expansion of hippocampal place fields \nduring route learning  [12].  Some of these theories  require relatively long temporal  win(cid:173)\ndows of synaptic plasticity (on the order of several hundreds of milliseconds) [4] while oth(cid:173)\ners have utilized temporal windows in the millisecond range for coincidence detection [3]. \nSequence learning in our model is based on a window of plasticity in the 10 to  15 ms range \nwhich is roughly consistent with recent physiological observations [2]  (see also [13)).  The \nidea that prediction and sequence learning may constitute an important goal of the neocortex \nhas previously been suggested in the context of statistical and information theoretic models \nof cortical processing [4, 5,6]. Our biophysical simulations suggest a possible implementa(cid:173)\ntion of such models in cortical circuitry. Given the universality ofthe problem of encoding \nand generating temporal sequences in both sensory and motor domains, the hypothesis of \npredictive sequence learning in recurrent neocortical circuits may help provide a unifying \nprinciple for studying cortical structure and function. \n\nReferences \n[1]  R.  1.  Douglas et al.,  Science  269, 981  (1995);  H. Suarez et aI., 1.  Neurosci.  15,6700 (1995); \nR. Maex and G.  A.  Orban, 1. Neurophysiol.  75,  1515 (1996); P. Mineiro and D. Zipser, Neural \nComput.  10, 353 (1998); F.  S. Chance et aI., Nature Neuroscience 2, 277 (1999). \n\n[2]  H. Markram et al.,  Science 275, 213  (1997); W.  B. Levy and O. Steward, Neuroscience 8, 791 \n(1983); D. Debanne et aI., Proc.  Natl. Acad. Sci. U.S.A. 91,  1148 (1994); L. I. Zhang et aI., Na(cid:173)\nture 395, 37 (1998); G.  Q. Bi and M.  M.  Poo, 1. 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