Replica-symmetric theory of nonlinear analogue neural networks

Abstract

On the basis of the theory of the naive mean field model of spin glasses, analogue neural networks of the Hopfield type are investigated in the saturation limit. The saddle-point equations for the order parameters describing retrieval and spin glass phases of the networks are obtained by means of a statistical mechanical analysis within the framework of the replica-symmetric theory and are shown to undergo a modification to that of AGS theory, due to the absence of the Onsager reaction term in the TAP equation. Based on the equations, the memory storage capacity of the networks is analysed as a function of the analogue gain beta . A small increase in the critical storage capacity is found for finite values of beta , compared with that of the Ising model networks with corresponding inverse temperature, although the qualitative nature of the phase diagram is unchanged.