| Issue |
J. Phys. I France
Volume 7, Number 2, February 1997
|
|
|---|---|---|
| Page(s) | 303 - 327 | |
| DOI | https://doi.org/10.1051/jp1:1997147 | |
DOI: 10.1051/jp1:1997147
J. Phys. I France 7 (1997) 303-327
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)
© Les Editions de Physique 1997
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. Krey21 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)
Abstract
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.
© Les Editions de Physique 1997