Replica symmetry breaking in neural networks: A few steps toward rigorous results
In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables) in order to work also with the Hopfield model (i.e. a pairwise mean-field neural-network whose couplings are drawn according to Hebb's learning rule): This is accomplished by grafting Guerra's telescopic averages on the transport equation technique, recently developed by some of the authors.