Variational Learning for Recurrent Spiking Networks

We derive a plausible learning rule for feedforward, feedback and lateral connections in a recurrent network of spiking neurons. Operating in the context of a generative model for distributions of spike sequences, the learning mechanism is derived from variational inference principles. The synaptic plasticity rules found are interesting in that they are strongly reminiscent of experimental Spike Time Dependent Plasticity, and in that they differ for excitatory and inhibitory neurons. A simulation confirms the method's applicability to learning both stationary and temporal spike patterns.

[1]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[2]  J. Hopfield,et al.  All-or-none potentiation at CA3-CA1 synapses. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Brendan J. Frey,et al.  Variational Learning in Nonlinear Gaussian Belief Networks , 1999, Neural Computation.

[4]  Michael I. Jordan,et al.  Learning with Mixtures of Trees , 2001, J. Mach. Learn. Res..

[5]  Michael I. Jordan,et al.  Bayesian parameter estimation via variational methods , 2000, Stat. Comput..

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

[7]  Wulfram Gerstner,et al.  Mathematical formulations of Hebbian learning , 2002, Biological Cybernetics.

[8]  Rajesh P. N. Rao Bayesian Computation in Recurrent Neural Circuits , 2004, Neural Computation.

[9]  Konrad Paul Kording,et al.  Bayesian integration in sensorimotor learning , 2004, Nature.

[10]  S. Wang,et al.  Graded bidirectional synaptic plasticity is composed of switch-like unitary events. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  J. Tenenbaum,et al.  Opinion TRENDS in Cognitive Sciences Vol.10 No.7 July 2006 Special Issue: Probabilistic models of cognition Theory-based Bayesian models of inductive learning and reasoning , 2022 .

[12]  Matthew J. Beal,et al.  Variational Bayesian learning of directed graphical models with hidden variables , 2006 .

[13]  Konrad Paul Kording,et al.  Review TRENDS in Cognitive Sciences Vol.10 No.7 July 2006 Special Issue: Probabilistic models of cognition Bayesian decision theory in sensorimotor control , 2022 .

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

[15]  Michael D. Lee,et al.  A Hierarchical Bayesian Model of Human Decision-Making on an Optimal Stopping Problem , 2006, Cogn. Sci..

[16]  Wulfram Gerstner,et al.  Predicting spike timing of neocortical pyramidal neurons by simple threshold models , 2006, Journal of Computational Neuroscience.

[17]  Karl J. Friston,et al.  Variational free energy and the Laplace approximation , 2007, NeuroImage.

[18]  L. Paninski,et al.  Common-input models for multiple neural spike-train data , 2007, Network.

[19]  Dan Cornford,et al.  Gaussian Process Approximations of Stochastic Differential Equations , 2007, Gaussian Processes in Practice.

[20]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[21]  Paul R. Schrater,et al.  Bayesian modeling of human sequential decision-making on the multi-armed bandit problem , 2008 .

[22]  Wei Ji Ma,et al.  Spiking networks for Bayesian inference and choice , 2008, Current Opinion in Neurobiology.

[23]  Wulfram Gerstner,et al.  Spike-response model , 2008, Scholarpedia.

[24]  Wolfgang Maass,et al.  STDP enables spiking neurons to detect hidden causes of their inputs , 2009, NIPS.

[25]  Kamiar Rahnama Rad,et al.  Mean-Field Approximations for Coupled Populations of Generalized Linear Model Spiking Neurons with Markov Refractoriness , 2009, Neural Computation.

[26]  Ian H. Stevenson,et al.  Bayesian Inference of Functional Connectivity and Network Structure From Spikes , 2009, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[27]  József Fiser,et al.  Spontaneous Cortical Activity Reveals Hallmarks of an Optimal Internal Model of the Environment , 2011, Science.