Effect of similarity between patterns in associative memory.

Abstract

We study the stability of patterns in Hopfield networks in which a part of memorized patterns are similar. The similarity between patterns impacts the stability of these patterns, but the stability of other independent patterns is only changed slightly. We show that the stability of patterns is affected in different ways by similarity. For networks storing a number of patterns, the similarity between patterns enhances the pattern stability. However, the stability of patterns can be weakened by the similarity when networks store fewer patterns, and the relation between the stability of patterns and similarity is nonmonotonic. We present a theoretical explanation of the effect of similarity on stability using signal-to-noise-ratio analysis.