Towards a learning-theoretic analysis of spike-timing dependent plasticity

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to theoretical analysis. We show that the selectron encodes reward estimates into spikes and that an error bound on spikes is controlled by a spiking margin and the sum of synaptic weights. Moreover, the efficacy of spikes (their usefulness to other reward maximizing selectrons) also depends on total synaptic strength. Finally, based on our analysis, we propose a regularized version of STDP, and show the regularization improves the robustness of neuronal learning when faced with multiple stimuli.

[1]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[2]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[3]  Geoffrey E. Hinton,et al.  Learning representations by back-propagation errors, nature , 1986 .

[4]  Elie Bienenstock,et al.  Neural Networks and the Bias/Variance Dilemma , 1992, Neural Computation.

[5]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Yoav Freund,et al.  Experiments with a New Boosting Algorithm , 1996, ICML.

[7]  Yoav Freund,et al.  Boosting the margin: A new explanation for the effectiveness of voting methods , 1997, ICML.

[8]  Yoav Freund,et al.  Large Margin Classification Using the Perceptron Algorithm , 1998, COLT' 98.

[9]  Peter L. Bartlett,et al.  Learning in Neural Networks: Theoretical Foundations , 1999 .

[10]  Peter L. Bartlett,et al.  Neural Network Learning - Theoretical Foundations , 1999 .

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

[12]  Naftali Tishby,et al.  The information bottleneck method , 2000, ArXiv.

[13]  H. Seung,et al.  Learning in Spiking Neural Networks by Reinforcement of Stochastic Synaptic Transmission , 2003, Neuron.

[14]  Sander M. Bohte,et al.  Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity , 2004, BNAIC.

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

[16]  Robert A. Legenstein,et al.  A Criterion for the Convergence of Learning with Spike Timing Dependent Plasticity , 2005, NIPS.

[17]  Pieter R. Roelfsema,et al.  Attention-Gated Reinforcement Learning of Internal Representations for Classification , 2005, Neural Computation.

[18]  L. Abbott,et al.  Cascade Models of Synaptically Stored Memories , 2005, Neuron.

[19]  S. Boucheron,et al.  Theory of classification : a survey of some recent advances , 2005 .

[20]  Karl J. Friston,et al.  A free energy principle for the brain , 2006, Journal of Physiology-Paris.

[21]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[22]  G. Tononi,et al.  Sleep function and synaptic homeostasis. , 2006, Sleep medicine reviews.

[23]  Robert A. Legenstein,et al.  Theoretical Analysis of Learning with Reward-Modulated Spike-Timing-Dependent Plasticity , 2007, NIPS.

[24]  Wolfgang Maass,et al.  Simplified Rules and Theoretical Analysis for Information Bottleneck Optimization and PCA with Spiking Neurons , 2007, NIPS.

[25]  Sander M. Bohte,et al.  Reducing the Variability of Neural Responses: A Computational Theory of Spike-Timing-Dependent Plasticity , 2007, Neural Computation.

[26]  L. Abbott,et al.  Limits on the memory storage capacity of bounded synapses , 2007, Nature Neuroscience.

[27]  Timothée Masquelier,et al.  Unsupervised Learning of Visual Features through Spike Timing Dependent Plasticity , 2007, PLoS Comput. Biol..

[28]  G. Tononi,et al.  Molecular and electrophysiological evidence for net synaptic potentiation in wake and depression in sleep , 2008, Nature Neuroscience.

[29]  G. Tononi,et al.  Cortical Firing and Sleep Homeostasis , 2009, Neuron.

[30]  Timothée Masquelier,et al.  Competitive STDP-Based Spike Pattern Learning , 2009, Neural Computation.

[31]  Klaus Pawelzik,et al.  Spike timing-dependent plasticity as dynamic filter , 2010, NIPS.

[32]  T. Sejnowski,et al.  Metabolic cost as a unifying principle governing neuronal biophysics , 2010, Proceedings of the National Academy of Sciences.

[33]  Alexander S. Ecker,et al.  Decorrelated Neuronal Firing in Cortical Microcircuits , 2010, Science.

[34]  G. Tononi,et al.  Sleep and wake modulate spine turnover in the adolescent mouse cortex , 2011, Nature Neuroscience.

[35]  Giulio Tononi,et al.  What can neurons do for their brain? Communicate selectivity with bursts , 2013, Theory in Biosciences.

[36]  Andrew Nere,et al.  A Neuromorphic Architecture for Object Recognition and Motion Anticipation Using Burst-STDP , 2012, PloS one.

[37]  David Balduzzi,et al.  Metabolic Cost as an Organizing Principle for Cooperative Learning , 2012, Adv. Complex Syst..