Learning algorithms with optimal stability in neural networks

Abstract

To ensure large basins of attraction in spin-glass-like neural networks of two-state elements xi imu =+or-1. The authors propose to study learning rules with optimal stability Delta , where delta is the largest number satisfying Delta <or=( Sigma j Jij xi jmu ) xi imu ; mu =1. . . . .p: i=1. . . . .N (where N is the number of neurons and p is the number of patterns). They motivate this proposal and provide optimal stability learning rules for two different choices of normalisation for the synaptic matrix (Jij). In addition, numerical work is presented which gives the value of the optimal stability for random uncorrelated patterns.