On the characteristics of the quadratic order associative memory that uses synchronous update and direct convergence

Abstract

A statistical method is applied to explore the characteristics of a certain class of quadratic order associative memories: the Synchronous Update Direct Convergence Memory (SQDM). The initial input vector is required to converge, with a given value of probability P-dc, to a stored codeword in just one synchronous update. The memory capacity m(s) is derived by using a figure of merit N Phi, and its tight asymptotic bound is found by using Tchebycheff's inequality. When the input contains erroneous bits, the maximum allowable number of attractors and their attraction radii are determined. The existence of principal connections T-pr useful in solving the problem of proliferation of connections in the SQDM is introduced. We prove that T-pr is a set of which an arbitrary connection T-ijk satisfies root m(s) less than or equal to \T-ijk\ less than or equal to 2 root m(s).