J. Phys. I France
Volume 7, Number 2, February 1997
Page(s) 303 - 327
DOI: 10.1051/jp1:1997147
J. Phys. I France 7 (1997) 303-327

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

F. Gerl1 and U. Krey2

1  Institut für Theoretische Physik der Universität Göttingen, Bunsenstrasse 9, 30373 Göttingen, Germany
2  Institut für Physik II der Universität Regensburg, Universitätsstrasse 31, 93040 Regensburg, Germany

(Received 10 July 1996, received in final form 29 November 1996, accepted 21 October 1996)

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.

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