Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity

Experimental 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 cortical adaptation.

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

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

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

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

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

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

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

[8]  Richard Hans Robert Hahnloser,et al.  Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit , 2000, Nature.

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

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

[11]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[12]  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.

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

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

[15]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

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

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

[18]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

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

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

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

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

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

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

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

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

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

[28]  Jean-Pascal Pfister,et al.  Optimal Spike-Timing-Dependent Plasticity for Precise Action Potential Firing in Supervised Learning , 2005, Neural Computation.

[29]  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.

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

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

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

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

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

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

[36]  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.

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

[38]  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.

[39]  Lucas C. Parra,et al.  Maximising Sensitivity in a Spiking Network , 2004, NIPS.

[40]  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.

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

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