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Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in simple and multilayer Perceptrons | | F. Gerl
; U. Krey
; | | Date: |
22 Oct 1996 | | Subject: | Disordered Systems and Neural Networks | cond-mat.dis-nn | | Affiliation: | Univ. Goettingen) and U. Krey (Univ. Regensburg | | 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. | | Source: | arXiv, cond-mat/9610165 | | Services: | Forum | Review | PDF | Favorites | |
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