Random Recurrent Neural Networks Dynamics

M. Samuelides 1 Bruno Cessac 2, 3
3 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
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}.
Type de document :
Article dans une revue
EPJ Special Topics, Springer, 2007, "Topics in Dynamical Neural Networks : From Large Scale Neural Networks to Motor Control and Vision", 142 (1), pp.89-122
Liste complète des métadonnées

https://hal.inria.fr/inria-00529560
Contributeur : Bruno Cessac <>
Soumis le : lundi 25 octobre 2010 - 21:07:35
Dernière modification le : vendredi 25 mai 2018 - 12:02:04

Lien texte intégral

Identifiants

Citation

M. Samuelides, Bruno Cessac. Random Recurrent Neural Networks Dynamics. EPJ Special Topics, Springer, 2007, "Topics in Dynamical Neural Networks : From Large Scale Neural Networks to Motor Control and Vision", 142 (1), pp.89-122. 〈inria-00529560〉

Partager

Métriques

Consultations de la notice

516