Stochastic firing rate models
Abstract
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network equations in a general setting, and we express here the results in a more customary and simpler framework. We propose a heuristic argument to derive these equations providing a more intuitive understanding of their origin. These equations are characterized by a strong coupling between the different moments of the solutions. We analyse the equations, present an algorithm to simulate the solutions of these mean-field equations, and investigate numerically the equations. In particular, we build a bridge between these equations and Sompolinsky and collaborators approach (1988, 1990), and show how the coupling between the mean and the covariance function deviates from customary approaches.
Cite
@article{arxiv.1001.3872,
title = {Stochastic firing rate models},
author = {Jonathan Touboul and Bard Ermentrout and Olivier Faugeras and Bruno Cessac},
journal= {arXiv preprint arXiv:1001.3872},
year = {2010}
}