Retrieval Properties of Bidirectional Associative Memories

We study a two-layer neural network made of N and M(N) neurons, producing a two-way association search for a family of p(N) patterns, where each pattern is a pair of two independent sub-categories of information having respectively N and M(N) components. In terms of the ratio γ=limN→∞M(N)/N, we study the retrieval capability of this network and show that there exists, at least, three regimes of association for which we determine the evolution of the threshold α c (γ) of the storage capacity α=limN→∞p(N)/N.