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Optimality Model of Unsupervised Spike-Timing-Dependent Plasticity: Synaptic Memory and Weight Distribution

taro.toyoizumi{at}brain.riken.jp School of Computer and Communication Sciences and Brain-Mind Institute, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne EPFL, Switzerland, and Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo 153-8505, Japan

Jean-Pascal Pfister

jean-pascal.pfister{at}epfl.ch School of Computer and Communication Sciences and Brain-Mind Institute, Ecole Polytechnique Fédérale de Lausanne, CH–1015 Lausanne EPFL, Switzerland

Kazuyuki Aihara

aihara{at}sat.t.u.-tokyo.ac.jp Department of Information and Systems, Institute of Industrial Science, University of Tokyo, 153–8505, Tokyo, Japan, and Aihara Complexity Modelling Project, ERATO, JST, Shibuya-ku, Tokyo 151–0064, Japan

Wulfram Gerstner

wulfram.gerstner{at}epfl.ch School of Computer and Communication Sciences and Brain-Mind Institute, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne EPFL, Switzerland

We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory.

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