The Effect of Synaptic Disconnection on the Performance of Hopfield Associative Memories

Abstract

Hopfield associative memories (HAMs) consisting of n (-1, +1) -binary neurons are considered. Each synaptic connection is assumed to be disconnected with probability q. Using the Galambos Poison limit theorem of order statistics, it is shown rigorously that HAMs with up to n²q randomly scattered synaptic disconnections have, with high probability, region of attractions of size ρn (ρn-error-correction capability) provided that they are not loaded with more than (1-2ρ) ² (1-q) n/2log (1-q) n² encoded patterns.