The B.A.M. Storage Capacity

The Bidirectional Associative Memory (B.A.M.) is a neural network which can store and associate pairs of data in the form of two patterns using an input network of $M$ neurons and an output network with $N$ neurons. Despite its interest there are no theoretical investigations about this model. We obtain the equations of state in a rigorous way using only the assumption that the Edwards-Anderson parameters associated to the two networks are self-averaging: this important property corresponds to the replica symmetry hypothesis in the replica calculations. A comparison between the methods used in the literature is made and the connection of our derivation with Peretto's method is shown. The storage capacity of the B.A.M. is computed when $N=M$ and a bound on it is derived when $N\neq M$, in contrast with the strongly diluted case in which the critical capacity is unbounded for $N/M\to 0$ or $\to \infty$