REPLICA-SYMMETRY BREAKING IN NEURAL NETWORKS

Replica-symmetry breaking is studied in fully connected neural networks with modified pseudo-inverse interactions. The interaction matrix has an intermediate form between the Hebb learning rule and the pseudo-inverse one. At low temperature there is a region of parameters where the replica-symmetric solution is stable while its entropy is negative. It indicates the existence of the alternative solution in which the replica symmetry is broken. A one-step replica-symmetry breaking solution is found and its properties are analyzed.