Performance Improvement fo Dynamical Associative Memories by Solving Linear Inequalities

A main problem with dynamical associative memories (DAMs) is that when memory patterns are stored, pseudo-memories (false fixed points and limit cycles) are also generated and they hinder proper association of input patterns. To overcome this problem, Hassoun proposed a heuristic method of reducing pseudomemories. In this method, DAMs are constructed such that a zero vector called "ground state" as well as stored patterns is stabilized and sparsely activated states (sparse patterns) converge to the ground state. Such dynamical properties of neural networks can be described with linear inequalities, and connection weights of networks are obtained by solving these inequalities using the Ho-Kashyap algorithm. In this paper, we propose an extended Hassoun model in which network dynamics are modified such that dense patterns, mixture patterns and inhibition patterns are also converged to the ground state. In simulations, we compare association performance of this extended Hassoun model with conventional associative memory models, and demonstrate the usefulness of our proposed model as a dynamical associative memory.