Random Recurrent Neural Networks Dynamics

TL;DR

This review explores the dynamics of large random recurrent neural networks, focusing on mean-field theory to predict network behavior, including chaos, across different models and neuron populations.

Contribution

It provides a comprehensive overview of mean-field approaches to analyze the macroscopic dynamics of large random recurrent neural networks, including applications to chaos prediction.

Findings

Mean-field theory effectively predicts network dynamics.

Chaotic regimes can be characterized in AFRRNN models.

Different neuron population structures influence network behavior.

Abstract

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using an averaging principle. After a first introductory section, the section 1 reviews the various models from the points of view of the single neuron dynamics and of the global network dynamics. A summary of notations is presented, which is quite helpful for the sequel. In section 2, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 3, some applications of mean-field theory to the prediction of chaotic regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The case of AFRRNN with an homogeneous population of neurons is studied in section 4. Then, a two-population model is studied in section 5. The occurrence of a cyclo-stationary chaos is displayed using the results of \cite{Dauce01}. In section 6, an insight of the application of mean-field theory to IF networks is given using the results of \cite{BrunelHakim99}.