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 MFT model, which is obtained by applying the mean field approximation to the Boltzmann machine, is a discrete-time recurrent neural network. We prove that the set of asymptotically stable fixed points of the asynchronous MFT model coincides with the set of asymptotically stable equilibria 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). Copyright (C) 1996 Elsevier Science Ltd.