Stochastic firing rate models

TL;DR

This paper reviews a stochastic mean-field approach to neural network modeling, emphasizing the coupling of moments, providing a simpler framework, and connecting it to classical methods with numerical analysis.

Contribution

It introduces a rigorous stochastic mean-field model for neural networks, simplifies its framework, and explores the coupling between moments, linking it to classical approaches.

Findings

The equations accurately describe stochastic neural dynamics.

Numerical simulations validate the theoretical model.

The approach reveals deviations from traditional mean-field methods.

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.