A computational theory of spike-timing dependent plasticity: achieving robust neural responses via conditional entropy minimization.

textabstractExperimental studies have observed synaptic potentiation when a presynaptic neuron fires shortly before a postsynaptic neuron, and synaptic depression when the presynaptic neuron fires shortly after. The dependence of synaptic modulation on the precise timing of the two action potentials is known as spike-timing dependent plasticity or STDP. We derive STDP from a simple computational principle: synapses adapt so as to minimize the postsynaptic neuron's variability to a given presynaptic input, causing the neuron's output to become more reliable in the face of noise. Using an entropy-minimization objective function and the biophysically realistic spike-response model of Gerstner (2001), we simulate neurophysiological experiments and obtain the characteristic STDP curve along with other phenomena including the reduction in synaptic plasticity as synaptic efficacy increases. We compare our account to other efforts to derive STDP from computational principles, and argue that our account provides the most comprehensive coverage of the phenomena. Thus, reliability of neural response in the face of noise may be a key goal of unsupervised cortical adaptation

[1]  G. Bi,et al.  Synaptic modification by correlated activity: Hebb's postulate revisited. , 2001, Annual review of neuroscience.

[2]  Mark C. W. van Rossum,et al.  Stable Hebbian Learning from Spike Timing-Dependent Plasticity , 2000, The Journal of Neuroscience.

[3]  D. Debanne,et al.  Long‐term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures , 1998, The Journal of physiology.

[4]  S. Schultz Principles of Neural Science, 4th ed. , 2001 .

[5]  Rajesh P. N. Rao,et al.  Predictive Sequence Learning in Recurrent Neocortical Circuits , 1999, NIPS.

[6]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

[7]  Gal Chechik,et al.  Spike-Timing-Dependent Plasticity and Relevant Mutual Information Maximization , 2003, Neural Computation.

[8]  Paul E. Hennion Algorithm 84: Simpson's integration , 1962, CACM.

[9]  W. Gerstner,et al.  Chapter 12 A framework for spiking neuron models: The spike response model , 2001 .

[10]  Peter Dayan,et al.  Plasticity Kernels and Temporal Statistics , 2003, NIPS.

[11]  P. J. Sjöström,et al.  Rate, Timing, and Cooperativity Jointly Determine Cortical Synaptic Plasticity , 2001, Neuron.

[12]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[13]  David B. Grayden,et al.  Spike-Timing-Dependent Plasticity: The Relationship to Rate-Based Learning for Models with Weight Dynamics Determined by a Stable Fixed Point , 2004, Neural Computation.

[14]  M. Poo,et al.  Calcium stores regulate the polarity and input specificity of synaptic modification , 2000, Nature.

[15]  J J Hopfield,et al.  Learning rules and network repair in spike-timing-based computation networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Robert A. Legenstein,et al.  What Can a Neuron Learn with Spike-Timing-Dependent Plasticity? , 2005, Neural Computation.

[17]  Florentin Wörgötter,et al.  How the Shape of Pre- and Postsynaptic Signals Can Influence STDP: A Biophysical Model , 2004, Neural Computation.

[18]  Eero P. Simoncelli,et al.  Comparing integrate-and-fire models estimated using intracellular and extracellular data , 2005, Neurocomputing.

[19]  Y. Dan,et al.  Spike Timing-Dependent Plasticity of Neural Circuits , 2004, Neuron.

[20]  Guo-Qiang Bi,et al.  Spatiotemporal specificity of synaptic plasticity: cellular rules and mechanisms , 2002, Biological Cybernetics.

[21]  D. Johnston,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997 .

[22]  Eugene M. Izhikevich,et al.  Relating STDP to BCM , 2003, Neural Computation.

[23]  Lucas C. Parra,et al.  Maximising Information yields Spike Timing Dependent Plasticity , 2005 .

[24]  Amos Storkey,et al.  Advances in Neural Information Processing Systems 20 , 2007 .

[25]  P. Dayan Matters temporal , 2002, Trends in Cognitive Sciences.

[26]  Xiaohui Xie,et al.  Learning in neural networks by reinforcement of irregular spiking. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Wulfram Gerstner,et al.  Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning , 2001, Neural Computation.

[28]  Rajesh P. N. Rao,et al.  Spike-Timing-Dependent Hebbian Plasticity as Temporal Difference Learning , 2001, Neural Computation.

[29]  D. Feldman,et al.  Timing-Based LTP and LTD at Vertical Inputs to Layer II/III Pyramidal Cells in Rat Barrel Cortex , 2000, Neuron.

[30]  Jean-Pascal Pfister,et al.  Spike-timing Dependent Plasticity and Mutual Information Maximization for a Spiking Neuron Model , 2004, NIPS.

[31]  L. Abbott,et al.  Homeostasis and Learning through Spike-Timing Dependent Plasticity , 2003 .

[32]  Li I. Zhang,et al.  A critical window for cooperation and competition among developing retinotectal synapses , 1998, Nature.

[33]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[34]  Wulfram Gerstner,et al.  Noise and the PSTH Response to Current Transients: I. General Theory and Application to the Integrate-and-Fire Neuron , 2001, Journal of Computational Neuroscience.

[35]  V. Han,et al.  Synaptic plasticity in a cerebellum-like structure depends on temporal order , 1997, Nature.

[36]  Florentin Wörgötter,et al.  Isotropic Sequence Order Learning , 2003, Neural Computation.

[37]  Jesper Tegnér,et al.  Spike-timing-dependent plasticity: common themes and divergent vistas , 2002, Biological Cybernetics.

[38]  Henry Markram,et al.  An Algorithm for Modifying Neurotransmitter Release Probability Based on Pre- and Postsynaptic Spike Timing , 2001, Neural Computation.

[39]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[40]  Rajesh P. N. Rao,et al.  Motion detection and prediction through spike-timing dependent plasticity , 2004 .

[41]  Wulfram Gerstner,et al.  Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity , 2004, BNAIC.

[42]  Patrick D. Roberts,et al.  Spike timing dependent synaptic plasticity in biological systems , 2002, Biological Cybernetics.

[43]  R. Kempter,et al.  Hebbian learning and spiking neurons , 1999 .

[44]  Rajesh P. N. Rao,et al.  Motion detection and prediction through spike-timing dependent plasticity. , 2004, Network.

[45]  Dean V. Buonomano,et al.  Mechanisms and significance of spike-timing dependent plasticity , 2002, Biological Cybernetics.

[46]  Y. Dan,et al.  Spike-timing-dependent synaptic modification induced by natural spike trains , 2002, Nature.