Determination of hopfield associative memory characteristics using a single parameter

Abstract

A new statistical method is proposed for exploring the characteristics of the Hopfield associative memory (HAM). The existence of an average signal-to-noise ratio parameter (which we call C) has been successfully applied to derive equations that are capable of concisely estimating the storage capacity of (a) direct convergence nets in which the initial vector is required to precisely converge to the memorized vector in one iteration and (b) indirect convergence nets in which a specified error ϵ is allowed after multiple iterations. The close tie between the memory capacity and the required convergence probability of the HAM is described. The significance of the 1-to-1 relationship between the indirect convergence probability and the parameter ϵ/η (η = probability of a neuron state being an incorrect bit) is shown. The importance of the parameter ηN in determining the capacity of the direct convergence nets is also discussed. The theory not only provides the memory capacity for various versions of the HAM, but it gives an explicit solution for the radius of attraction parameter.