{"title": "Learning in Silicon: Timing is Everything", "book": "Advances in Neural Information Processing Systems", "page_first": 75, "page_last": 82, "abstract": "", "full_text": "Learning in Silicon: Timing is Everything\n\nJohn V. Arthur and Kwabena Boahen\n\nDepartment of Bioengineering\n\nUniversity of Pennsylvania\n\n{jarthur, boahen}@seas.upenn.edu\n\nPhiladelphia, PA 19104\n\nAbstract\n\nWe describe a neuromorphic chip that uses binary synapses with spike\ntiming-dependent plasticity (STDP) to learn stimulated patterns of activ-\nity and to compensate for variability in excitability. Speci\ufb01cally, STDP\npreferentially potentiates (turns on) synapses that project from excitable\nneurons, which spike early, to lethargic neurons, which spike late. The\nadditional excitatory synaptic current makes lethargic neurons spike ear-\nlier, thereby causing neurons that belong to the same pattern to spike in\nsynchrony. Once learned, an entire pattern can be recalled by stimulating\na subset.\n\n1 Variability in Neural Systems\n\nEvidence suggests precise spike timing is important in neural coding, speci\ufb01cally, in the\nhippocampus. The hippocampus uses timing in the spike activity of place cells (in addition\nto rate) to encode location in space [1]. Place cells employ a phase code: the timing at\nwhich a neuron spikes relative to the phase of the inhibitory theta rhythm (5-12Hz) conveys\ninformation. As an animal approaches a place cell\u2019s preferred location, the place cell not\nonly increases its spike rate, but also spikes at earlier phases in the theta cycle.\n\nTo implement a phase code, the theta rhythm is thought to prevent spiking until the input\nsynaptic current exceeds the sum of the neuron threshold and the decreasing inhibition on\nthe downward phase of the cycle [2]. However, even with identical inputs and common\ntheta inhibition, neurons do not spike in synchrony. Variability in excitability spreads the\nactivity in phase. Lethargic neurons (such as those with high thresholds) spike late in the\ntheta cycle, since their input exceeds the sum of the neuron threshold and theta inhibition\nonly after the theta inhibition has had time to decrease. Conversely, excitable neurons\n(such as those with low thresholds) spike early in the theta cycle. Consequently, variability\nin excitability translates into variability in timing.\n\nWe hypothesize that the hippocampus achieves its precise spike timing (about 10ms)\nthrough plasticity enhanced phase-coding (PEP). The source of hippocampal timing preci-\nsion in the presence of variability (and noise) remains unexplained. Synaptic plasticity can\ncompensate for variability in excitability if it increases excitatory synaptic input to neurons\nin inverse proportion to their excitabilities. Recasting this in a phase-coding framework, we\ndesire a learning rule that increases excitatory synaptic input to neurons directly related to\ntheir phases. Neurons that lag require additional synaptic input, whereas neurons that lead\n\n\f\u0006\n\u0005\n\u001e\n \n\u001f\n\nB\n\n\u001f'\u001e\u0005\u0006\n\nA\n\nFigure 1: STDP Chip. A The chip has a 16-by-16 array of microcircuits; one microcircuit\nincludes four principal neurons, each with 21 STDP circuits. B The STDP Chip is em-\nbedded in a circuit board including DACs, a CPLD, a RAM chip, and a USB chip, which\ncommunicates with a PC.\n\nrequire none. The spike timing-dependent plasticity (STDP) observed in the hippocampus\nsatis\ufb01es this requirement [3]. It requires repeated pre-before-post spike pairings (within a\ntime window) to potentiate and repeated post-before-pre pairings to depress a synapse.\n\nHere we validate our hypothesis with a model implemented in silicon, where variability is\nas ubiquitous as it is in biology [4]. Section 2 presents our silicon system, including the\nSTDP Chip. Section 3 describes and characterizes the STDP circuit. Section 4 demon-\nstrates that PEP compensates for variability and provides evidence that STDP is the com-\npensation mechanism. Section 5 explores a desirable consequence of PEP: unconventional\nassociative pattern recall. Section 6 discusses the implications of the PEP model, including\nits bene\ufb01ts and applications in the engineering of neuromorphic systems and in the study\nof neurobiology.\n\n2 Silicon System\n\nWe have designed, submitted, and tested a silicon implementation of PEP. The STDP Chip\nwas fabricated through MOSIS in a 1P5M 0.25\u00b5m CMOS process, with just under 750,000\ntransistors in just over 10mm2 of area. It has a 32 by 32 array of excitatory principal neu-\nrons commingled with a 16 by 16 array of inhibitory interneurons that are not used here\n(Figure 1A). Each principal neuron has 21 STDP synapses. The address-event representa-\ntion (AER) [5] is used to transmit spikes off chip and to receive afferent and recurrent spike\ninput.\n\nTo con\ufb01gure the STDP Chip as a recurrent network, we embedded it in a circuit board (Fig-\nure 1B). The board has \ufb01ve primary components: a CPLD (complex programmable logic\ndevice), the STDP Chip, a RAM chip, a USB interface chip, and DACs (digital-to-analog\nconverters). The central component in the system is the CPLD. The CPLD handles AER\ntraf\ufb01c, mediates communication between devices, and implements recurrent connections\nby accessing a lookup table, stored in the RAM chip. The USB interface chip provides\na bidirectional link with a PC. The DACs control the analog biases in the system, includ-\ning the leak current, which the PC varies in real-time to create the global inhibitory theta\nrhythm.\n\nThe principal neuron consists of a refractory period and calcium-dependent potassium cir-\ncuit (RCK), a synapse circuit, and a soma circuit (Figure 2A). RCK and the synapse are\n\n\f4+\u0004\n\n)0\n\n2\u0006IJIO\u0006\u0002\n5FE\u0006A\n\n15\u0004\u0004)\n\n5\u0006\u0006=\n\n5O\u0006=FIA\n\n56,2\n\n2HAIO\u0006\u0002\n5FE\u0006A\n\nA\n\n2-\n\n\u00042.\n\nH\nA\nJ\nI\n=\n4\n\n\u001e\n\n\u001e\u0002\u001f\n\n\u001e\u0002\u001e&\n\n\u001e\u0002\u001e$\n\n\u001e\u0002\u001e\"\n\n\u001e\u0002\u001e \n\n\u001e\n\n\u001e\n\nO\nJ\nE\n\u0006\nE\n\n>\n=\n>\n\u0006\nH\nF\n\n\u0014\n\nE\n\nA\n\u0006\nF\n5\n\nB\n\n2HAIO\u0006\u0002\n5FE\u0006A\n\n\u001e\u0002\u001e#\n\n\u001e\u0002\u001f\n\n\u001e\u0002\u001e#\n6E\u0006A\u001cI\u001d\n\n\u001e\u0002\u001f\n\nFigure 2: Principal neuron. A A simpli\ufb01ed schematic is shown, including: the synapse,\nrefractory and calcium-dependent potassium channel (RCK), soma, and axon-hillock (AH)\ncircuits, plus their constituent elements, the pulse extender (PE) and the low-pass \ufb01lter\n(LPF). B Spikes (dots) from 81 principal neurons are temporally dispersed, when excited\nby poisson-like inputs (58Hz) and inhibited by the common 8.3Hz theta rhythm (solid line).\nThe histogram includes spikes from \ufb01ve theta cycles.\n\ncomposed of two reusable blocks: the low-pass \ufb01lter (LPF) and the pulse extender (PE).\nThe soma is a modi\ufb01ed version of the LPF, which receives additional input from an axon-\nhillock circuit (AH).\n\nRCK is inhibitory to the neuron. It consists of a PE, which models calcium in\ufb02ux during\na spike, and a LPF, which models calcium buffering. When AH \ufb01res a spike, a packet of\ncharge is dumped onto a capacitor in the PE. The PE\u2019s output activates until the charge\ndecays away, which takes a few milliseconds. Also, while the PE is active, charge accu-\nmulates on the LPF\u2019s capacitor, lowering the LPF\u2019s output voltage. Once the PE deacti-\nvates, this charge leaks away as well, but this takes tens of milliseconds because the leak is\nsmaller. The PE\u2019s and the LPF\u2019s inhibitory effects on the soma are both described below\nin terms of the sum (ISHUNT) of the currents their output voltages produce in pMOS tran-\nsistors whose sources are at Vdd (see Figure 2A). Note that, in the absence of spikes, these\ncurrents decay exponentially, with a time-constant determined by their respective leaks.\n\nThe synapse circuit is excitatory to the neuron. It is composed of a PE, which represents\nthe neurotransmitter released into the synaptic cleft, and a LPF, which represents the bound\nneurotransmitter. The synapse circuit is similar to RCK in structure but differs in function:\nIt is activated not by the principal neuron itself but by the STDP circuits (or directly by\nafferent spikes that bypass these circuits, i.e., \ufb01xed synapses). The synapse\u2019s effect on the\nsoma is also described below in terms of the current (ISYN) its output voltage produces in a\npMOS transistor whose source is at Vdd.\n\nThe soma circuit is a leaky integrator. It receives excitation from the synapse circuit and\nshunting inhibition from RCK and has a leak current as well.\nIts temporal behavior is\ndescribed by:\n\n\u03c4\n\ndISOMA\n\ndt\n\n+ ISOMA = ISYN I0\nISHUNT\n\nwhere ISOMA is the current the capacitor\u2019s voltage produces in a pMOS transistor whose\nsource is at Vdd (see Figure 2A). ISHUNT is the sum of the leak, refractory, and calcium-\ndependent potassium currents. These currents also determine the time constant: \u03c4 =\n\n, where I0 and \u03ba are transistor parameters and Ut is the thermal voltage.\n\nC Ut\n\n\u03baISHUNT\n\n\f,A?=O\n\n1\u0006JACH=J\u0006H\n\n56,2\u0014?EH?KEJ\n\n\u0007\u000462\n\n\u0007\u00046,\n\n54)\u0004\n\n2HAIO\u0006=FJE?\u0014IFE\u0006A\nA\n\n2\u0006IJIO\u0006=FJE?\u0014IFE\u0006A\n\nI\nC\n\u0006\nE\nH\nE\n=\nF\n\u0014\nB\n\u0006\n\u0014\nH\nA\n>\n\u0006\nK\n\u0006\n\u0014\nA\nI\nH\nA\nL\n\u0006\n1\n\nB\n\n2\u0006JA\u0006JE=JE\u0006\u0006\n\n\u0014\u0014\u001e\u0002\u001f\n\n\u0014\u001e\u0002\u001e#\n\n\u0014\u0014\u0014\u0014\u001e\n\n\u0014\u0014\u001e\u0002\u001e#\n\n\u0014\u0014\u0014\u001e\u0002\u001f\n\n,AFHAIIE\u0006\u0006\n\u0002&\u001e\n\u0002\"\u001e\n\n2HAIO\u0006=FJE?\u0014IFE\u0006A\n2\u0006IJIO\u0006=FJE?\u0014IFE\u0006A\n\n\u001e\n\n\"\u001e\n\n&\u001e\n\n5FE\u0006A\u0014JE\u0006E\u0006C\u0003\u0014JFHA \u0014\u0002\u0014J F\u0006IJ \u001c\u0006I\u001d\n\nFigure 3: STDP circuit design and characterization. A The circuit is composed of three\nsubcircuits: decay, integrator, and SRAM. B The circuit potentiates when the presynaptic\nspike precedes the postsynaptic spike and depresses when the postsynaptic spike precedes\nthe presynaptic spike.\n\nThe soma circuit is connected to an AH, the locus of spike generation. The AH consists\nof model voltage-dependent sodium and potassium channel populations (modi\ufb01ed from [6]\nby Kai Hynna). It initiates the AER signaling process required to send a spike off chip.\n\nTo characterize principal neuron variability, we excited 81 neurons with poisson-like 58Hz\nspike trains (Figure 2B). We made these spike trains poisson-like by starting with a regular\n200Hz spike train and dropping spikes randomly, with probability of 0.71. Thus spikes\nwere delivered to neurons that won the coin toss in synchrony every 5ms. However, neurons\ndid not lock onto the input synchrony due to \ufb01ltering by the synaptic time constant (see\nFigure 2B). They also received a common inhibitory input at the theta frequency (8.3Hz),\nvia their leak current. Each neuron was prevented from \ufb01ring more than one spike in a theta\ncycle by its model calcium-dependent potassium channel population.\n\nThe principal neurons\u2019 spike times were variable. To quantify the spike variability, we used\ntiming precision, which we de\ufb01ne as twice the standard deviation of spike times accumu-\nlated from \ufb01ve theta cycles. With an input rate of 58Hz the timing precision was 34ms.\n\n3 STDP Circuit\n\nThe STDP circuit (related to [7]-[8]), for which the STDP Chip is named, is the most\nabundant, with 21,504 copies on the chip. This circuit is built from three subcircuits:\ndecay, integrator, and SRAM (Figure 3A). The decay and integrator are used to implement\npotentiation, and depression, in a symmetric fashion. The SRAM holds the current binary\nstate of the synapse, either potentiated or depressed.\n\nFor potentiation, the decay remembers the last presynaptic spike. Its capacitor is charged\nwhen that spike occurs and discharges linearly thereafter. A postsynaptic spike samples the\ncharge remaining on the capacitor, passes it through an exponential function, and dumps\nthe resultant charge into the integrator. This charge decays linearly thereafter. At the time\nof the postsynaptic spike, the SRAM, a cross-coupled inverter pair, reads the voltage on the\nintegrator\u2019s capacitor. If it exceeds a threshold, the SRAM switches state from depressed\nto potentiated (\u223cLTD goes high and \u223cLTP goes low). The depression side of the STDP\ncircuit is exactly symmetric, except that it responds to postsynaptic activation followed by\npresynaptic activation and switches the SRAM\u2019s state from potentiated to depressed (\u223cLTP\ngoes high and \u223cLTD goes low). When the SRAM is in the potentiated state, the presynaptic\n\n\fBefore STDP\n\nAfter STDP\n\n0\n0\n1\n\n2\n9\n\n3\n8\n\n5\n7\n\n7\n6\n\n8\n5\n\n0\n5\n\n*AB\u0006HA\u001456,2\n)BJAH\u001456,2\n\n#\u001e\n\n\"\u001e\n\n!\u001e\n\n \u001e\n\n\u001f\u001e\n\n\u001d\nI\n\u0006\n\u001c\n\u0006\n\u0006\nI\n?\nA\nH\nF\nC\n\u0006\n\u0006\n6\n\n\u0014\n\nE\n\nE\n\nE\n\nE\n\n\u001e\n\n#\u001e\n\nB\n\n$\u001e\n\n%\u001e\n\n&\u001e\n\n'\u001e\n\n\u001f\u001e\u001e\n\n1\u0006FKJ\u0014H=JA\u001c0\u0007\u001d\n\nJANJ\n\nA\n\n0.2\n\n0.4\n\n0.6\n\nTime(s)\n\n0.2\n\n0.4\nTime(s)\n\n0.6\n\nC\n\nFigure 4: Plasticity enhanced phase-coding. A Spike rasters of 81 neurons (9 by 9 cluster)\ndisplay synchrony over a two-fold range of input rates after STDP. B The degree of en-\nhancement is quanti\ufb01ed by timing precision. C Each neuron (center box) sends synapses to\n(dark gray) and receives synapses from (light gray) twenty-one randomly chosen neighbors\nup to \ufb01ve nodes away (black indicates both connections).\n\nspike activates the principal neuron\u2019s synapse; otherwise the spike has no effect.\n\nWe characterized the STDP circuit by activating a plastic synapse and a \ufb01xed synapse\u2013\nwhich elicits a spike at different relative times. We repeated this pairing at 16Hz. We\ncounted the number of pairings required to potentiate (or depress) the synapse. Based\non this count, we calculated the ef\ufb01cacy of each pairing as the inverse number of pair-\nings required (Figure 3B). For example, if twenty pairings were required to potentiate the\nsynapse, the ef\ufb01cacy of that pre-before-post time-interval was one twentieth. The ef\ufb01cacy\nof both potentiation and depression are \ufb01t by exponentials with time constants of 11.4ms\nand 94.9ms, respectively. This behavior is similar to that observed in the hippocampus:\npotentiation has a shorter time constant and higher maximum ef\ufb01cacy than depression [3].\n\n4 Recurrent Network\n\nWe carried out an experiment designed to test the STDP circuit\u2019s ability to compensate for\nvariability in spike timing through PEP. Each neuron received recurrent connections from\n21 randomly selected neurons within an 11 by 11 neighborhood centered on itself (see\nFigure 4C). Conversely, it made recurrent connections to randomly chosen neurons within\nthe same neighborhood. These connections were mediated by STDP circuits, initialized to\nthe depressed state. We chose a 9 by 9 cluster of neurons and delivered spikes at a mean\nrate of 50 to 100Hz to each one (dropping spikes with a probability of 0.75 to 0.5 from a\nregular 200Hz train) and provided common theta inhibition as before.\n\nWe compared the variability in spike timing after \ufb01ve seconds of learning with the initial\ndistribution. Phase coding was enhanced after STDP (Figure 4A). Before STDP, spike\ntiming among neurons was highly variable (except for the very highest input rate). After\nSTDP, variability was virtually eliminated (except for the very lowest input rate). Initially,\nthe variability, characterized by timing precision, was inversely related to the input rate,\ndecreasing from 34 to 13ms. After \ufb01ve seconds of STDP, variability decreased and was\nlargely independent of input rate, remaining below 11ms.\n\n\f #\n\n \u001e\n\n\u001f#\n\n\u001f\u001e\n\n#\n\n\u001e\n\nI\nA\nI\nF\n=\n\u0006\nO\nI\n\u0014\n@\nA\nJ\n=\nE\nJ\n\u0006\nA\nJ\n\u0006\n2\n\nB\n\nA\n\n5O\u0006=FJE?\u0014IJ=JA\n=BJAH\u001456,2\n\n#\u001e\n\n\u001f\u001e\u001e\n\n\u001f#\u001e\n\n \u001e\u001e\n\n #\u001e\n\n5FE\u0006E\u0006C\u0014\u0006H@AH\n\nFigure 5: Compensating for variability. A Some synapses (dots) become potentiated (light)\nwhile others remain depressed (dark) after STDP. B The number of potentiated synapses\nneurons make (pluses) and receive (circles) is negatively (r = -0.71) and positively (r =\n0.76) correlated to their rank in the spiking order, respectively.\n\nComparing the number of potentiated synapses each neuron made or received with its ex-\ncitability con\ufb01rmed the PEP hypothesis (i.e., leading neurons provide additional synaptic\ncurrent to lagging neurons via potentiated recurrent synapses). In this experiment, to elim-\ninate variability due to noise (as opposed to excitability), we provided a 17 by 17 cluster\nof neurons with a regular 200Hz excitatory input. Theta inhibition was present as before\nand all synapses were initialized to the depressed state. After 10 seconds of STDP, a large\nfraction of the synapses were potentiated (Figure 5A). When the number of potentiated\nsynapses each neuron made or received was plotted versus its rank in spiking order (Figure\n5B), a clear correlation emerged (r = -0.71 or 0.76, respectively). As expected, neurons that\nspiked early made more and received fewer potentiated synapses. In contrast, neurons that\nspiked late made fewer and received more potentiated synapses.\n\n5 Pattern Completion\n\nAfter STDP, we found that the network could recall an entire pattern given a subset, thus\nthe same mechanisms that compensated for variability and noise could also compensate\nfor lack of information. We chose a 9 by 9 cluster of neurons as our pattern and delivered\na poisson-like spike train with mean rate of 67Hz to each one as in the \ufb01rst experiment.\nTheta inhibition was present as before and all synapses were initialized to the depressed\nstate. Before STDP, we stimulated a subset of the pattern and only neurons in that subset\nspiked (Figure 6A). After \ufb01ve seconds of STDP, we stimulated the same subset again. This\ntime they recruited spikes from other neurons in the pattern, completing it (Figure 6B).\n\nUpon varying the fraction of the pattern presented, we found that the fraction recalled\nincreased faster than the fraction presented. We selected subsets of the original pattern\nrandomly, varying the fraction of neurons chosen from 0.1 to 1.0 (ten trials for each). We\nclassi\ufb01ed neurons as active if they spiked in the two second period over which we recorded.\nThus, we characterized PEP\u2019s pattern-recall performance as a function of the probability\nthat the pattern in question\u2019s neurons are activated (Figure 6C). At a fraction of 0.50 pre-\nsented, nearly all of the neurons in the pattern are consistently activated (0.91\u00b10.06), show-\ning robust pattern completion. We \ufb01tted the recall performance with a sigmoid that reached\n0.50 recall fraction with an input fraction of 0.30. No spurious neurons were activated dur-\ning any trials.\n\n\f4=JA\u001c0\u0007\u001d\n\n4=JA\u001c0\u0007\u001d\n\n\u001f\n\n&\n\n%\n\n$\n\n#\n\n\"\n\n!\n\n \n\n\u001f\n\n\u001e\n\nA\n\n\u0004AJM\u0006H\u0006\u0014=?JELEJO\n>AB\u0006HA\u001456,2\n\nB\n\n\u0004AJM\u0006H\u0006\u0014=?JELEJO\n=BJAH\u001456,2\n\n&\n\n%\n\n$\n\n#\n\n\"\n\n!\n\n \n\n\u001f\n\n\u001e\n\n@\nA\nL\nE\nJ\n?\n=\n\n\u0014\n\n\u0006\nH\nA\n\nJ\nJ\n\n=\nF\n\n\u0014\nB\n\n\u0006\n\n\u0014\n\n\u0006\n\u0006\n\nE\nJ\n?\n=\nH\n.\n\n\u001e\u0002&\n\n\u001e\u0002$\n\n\u001e\u0002\"\n\n\u001e\u0002 \n\n\u001e\n\n\u001e\n\nC\n\n\u001e\u0002 \n.H=?JE\u0006\u0006\u0014\u0006B\u0014F=JJAH\u0006\u0014IJE\u0006K\u0006=JA@\n\n\u001e\u0002\"\n\n\u001e\u0002$\n\n\u001e\u0002&\n\n\u001f\n\nFigure 6: Associative recall. A Before STDP, half of the neurons in a pattern are stimulated;\nonly they are activated. B After STDP, half of the neurons in a pattern are stimulated, and\nall are activated. C The fraction of the pattern activated grows faster than the fraction\nstimulated.\n\n6 Discussion\n\nOur results demonstrate that PEP successfully compensates for graded variations in our sil-\nicon recurrent network using binary (on\u2013off) synapses (in contrast with [8], where weights\nare graded). While our chip results are encouraging, variability was not eliminated in every\ncase. In the case of the lowest input (50Hz), we see virtually no change (Figure 4A). We\nsuspect the timing remains imprecise because, with such low input, neurons do not spike\nevery theta cycle and, consequently, provide fewer opportunities for the STDP synapses to\npotentiate. This shortfall illustrates the system\u2019s limits; it can only compensate for variabil-\nity within certain bounds, and only for activity appropriate to the PEP model.\n\nAs expected, STDP is the mechanism responsible for PEP. STDP potentiated recurrent\nsynapses from leading neurons to lagging neurons, reducing the disparity among the di-\nverse population of neurons. Even though the STDP circuits are themselves variable, with\ndifferent ef\ufb01cacies and time constants, when using timing the sign of the weight-change\nis always correct (data not shown). For this reason, we chose STDP over other more\nphysiological implementations of plasticity, such as membrane-voltage-dependent plastic-\nity (MVDP), which has the capability to learn with graded voltage signals [9], such as those\nfound in active dendrites, providing more computational power [10].\n\nPreviously, we investigated a MVDP circuit, which modeled a voltage-dependent NMDA-\nreceptor-gated synapse [11]. It potentiated when the calcium current analog exceeded a\nthreshold, which was designed to occur only during a dendritic action potential. This circuit\nproduced behavior similar to STDP, implying it could be used in PEP. However, it was\nsensitive to variability in the NMDA and potentiation thresholds, causing a fraction of the\npopulation to potentiate anytime the synapse received an input and another fraction to never\npotentiate, rendering both subpopulations useless. Therefore, the simpler, less biophysical\nSTDP circuit won out over the MVDP circuit: In our system timing is everything.\n\nAssociative storage and recall naturally emerge in the PEP network when synapses between\nneurons coactivated by a pattern are potentiated. These synapses allow neurons to recruit\ntheir peers when a subset of the pattern is presented, thereby completing the pattern. How-\never, this form of pattern storage and completion differs from Hop\ufb01eld\u2019s attractor model\n[12] . Rather than forming symmetric, recurrent neuronal circuits, our recurrent network\nforms asymmetric circuits in which neurons make connections exclusively to less excitable\nneurons in the pattern. In both the poisson-like and regular cases (Figures 4 & 5), only\nabout six percent of potentiated connections were reciprocated, as expected by chance. We\nplan to investigate the storage capacity of this asymmetric form of associative memory.\n\nOur system lends itself to modeling brain regions that use precise spike timing, such as\n\n\fthe hippocampus. We plan to extend the work presented to store and recall sequences of\npatterns, as the hippocampus is hypothesized to do. Place cells that represent different\nlocations spike at different phases of the theta cycle, in relation to the distance to their pre-\nferred locations. This sequential spiking will allow us to link patterns representing different\nlocations in the order those locations are visited, thereby realizing episodic memory.\n\nWe propose PEP as a candidate neural mechanism for information coding and storage in the\nhippocampal system. Observations from the CA1 region of the hippocampus suggest that\nbasal dendrites (which primarily receive excitation from recurrent connections) support\nsubmillisecond timing precision, consistent with PEP [13]. We have shown, in a silicon\nmodel, PEP\u2019s ability to exploit such fast recurrent connections to sharpen timing precision\nas well as to associatively store and recall patterns.\n\nAcknowledgments\n\nWe thank Joe Lin for assistance with chip generation. The Of\ufb01ce of Naval Research funded\nthis work (Award No. N000140210468).\n\nReferences\n\n[1] O\u2019Keefe J. & Recce M.L. (1993). Phase relationship between hippocampal place units and the\nEEG theta rhythm. Hippocampus 3(3):317-330.\n\n[2] Mehta M.R., Lee A.K. & Wilson M.A. (2002) Role of experience and oscillations in transforming\na rate code into a temporal code. Nature 417(6890):741-746.\n\n[3] Bi G.Q. & Wang H.X. 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