Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in Simple and Multilayer Perceptrons

F. Gerl , U. Krey

Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the critical loading, and (ii) the case of two-layer AND-perceptrons, if one learns with maximal stability. We find that the deviation of our cavity solution from the replica symmetric one in these cases is a clear indication of the necessity of replica symmetry breaking. In any case the cavity solution tends to underestimate the storage capabilities of the networks.

Domaines: Articles anciens

F. Gerl, U. Krey. Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in Simple and Multilayer Perceptrons. Journal de Physique I, 1997, 7 (2), pp.303-327. ⟨10.1051/jp1:1997147⟩. ⟨jpa-00247330⟩