Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in simple   and multilayer Perceptrons
  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. 
F. Gerl (Univ. Goettingen) and U. Krey (Univ. Regensburg)