ON THE HOPFIELD NEURAL NETWORKS AND MEAN-FIELD THEORY

In this paper, we analyse mathematically the relationship between the mean field theory network (MFT) model and the continuous-time Hopfield neural network by the use of the theory of dynamical systems. This MF T model, which is obtained by applying the mean field approximation to the Boltzmann machine, is a discrete-time recurrent neural network. W e prove that the set of asymptotically stable fixed points of the asyn chronous MFT model coincides with the set of asymptotically stable equ ilibria of the continuous-time Hopfield neural network. Therefore, it is shown that the asynchronous MFT model is equivalent to the Hopfield neural network on the nature of the fixed points (or equilibria). Cop yright (C) 1996 Elsevier Science Ltd.