Lower bounds on the restitution error in the Hopfield Model

Abstract

This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let $m$ denote the number of stored patterns and $N$ that of neurons. Assuming that $m/N\to \alpha$ as $N\to\infty $ we show that for $\alpha>0$ the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as $\alpha\to\infty $ .