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Stochastic dynamics of a finite-size spiking neural network

Hédi Soula 1, 2 Carson C Chow 3
1 BEAGLE - Artificial Evolution and Computational Biology
LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558, Inria Grenoble - Rhône-Alpes, LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution, mean rate, variance, and autocorrelation function of the network activity. The model is applicable to any network where the probability of firing of a neuron in the network depends on only the number of neurons that fired in a previous temporal epoch. Networks with statistically homogeneous connectivity and membrane and synaptic time constants that are not excessively long could satisfy these conditions. Our model completely accounts for the size of the network and correlations in the firing activity. It also allows us to examine how the network dynamics can deviate from mean field theory. We show that the model and solutions are applicable to spiking neural networks in biophysically plausible parameter regimes.
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Submitted on : Friday, November 30, 2012 - 6:30:28 PM
Last modification on : Tuesday, July 20, 2021 - 5:20:04 PM

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Hédi Soula, Carson C Chow. Stochastic dynamics of a finite-size spiking neural network. Neural Computation, Massachusetts Institute of Technology Press (MIT Press), 2006, 19 (12), pp.3262-92. ⟨10.1162/neco.2007.19.12.3262⟩. ⟨hal-00759513⟩