J. Phys. I France
Volume 5, Numéro 1, January 1995
Page(s) 85 - 96
DOI: 10.1051/jp1:1995116
J. Phys. I France 5 (1995) 85-96

The B.A.M. Storage Capacity

H. Englisch1, V. Mastropietro2 and B. Tirozzi3

1  Universität Leipzig, Inst. Für Informatik, D-04109 Leipzig, Germany
2  Dipartimento di Fisica, Università di Pisa, 56100 Pisa, Italia
3  Dipartimento di Matematica, Universita' di Roma "La Sapienza", 00185 Italia

(Received 22 February 1994, revised 23 September 1994, accepted 4 October 1994)

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 $\to \infty$.

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