Analysis of the Recalling Processes of Associative Memory by an Integral Representation of the Sign Function

The recalling processes of associative memory proposed by Amari and Maginu are analyzed without any assumption on asymptotic distributions of noise using an integral representation of the sign function and by introducing extra variables. General procedures for calculating mean of direction cosine a(t) between a certain memory s(1) and the state x(t) at time t are developed and the exact formulas for E[a(t)] are obtained up to t = 3. It is shown explicitly that E[a(3)] involves non-Gaussian effects caused by some self-coherences. In an approximation of neglecting all the self-coherent effects, general formulas for E[a(t)] are obtained. Copyright 1996 Published by Elsevier Science Ltd