Replica symmetry breaking in neural networks with modified pseudo-inverse interactions

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 temperatures there is a region of parameters where the replica symmetric solution is stable while its entropy is negative. It indicates the existence of an alternative solution in which the replica symmetry is broken. The one-step replica symmetry-breaking solution is found and its properties are analysed.