Random recurrent neural networks dynamics
École Nationale Supérieure de l'Aéronautique et de l'espace and ONERA/DTIM, 2 Av. E. Belin, 31055 Toulouse, France
2 INRIA, 2004 route des Lucioles, 06902 Sophia-Antipolis, France
3 INLN, 1361 route des Lucioles, 06560 Valbonne, France
4 Université de Nice, Parc Valrose, 06000 Nice, France
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are varying 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 2 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 3, mean-field dynamics is developed. The probability distribution characterizing global dynamics is computed. In section 4, 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 4.1. Then, a two-population model is studied in section 4.2. The occurrence of a cyclo-stationary chaos is displayed using the results of . In section 5, an insight of the application of mean-field theory to IF networks is given using the results of .
© EDP Sciences, Springer-Verlag, 2007