Statistical mechanics of Hopfield-like neural networks with modified interactions

Abstract

Hopfield-like neural networks (1982) with modified interactions are studied by a mean-field theory. The modification of interactions is achieved during a special thermally noised iterative procedure. The resulting couplings have an intermediate form between the Hebb-like learning rule and the pseudo inverse one. Replica-symmetric free energy of the model is obtained. Statistical properties of the model depend on three parameters: reduced number of the stored patterns alpha , reduced number of iteration steps of the modification procedure lambda and the temperature T. The phase diagram in the space of these parameters is obtained. The network can retrieve patterns at T=0 for alpha < alphac(lambda), where alphac(0) approximately= 0.14 and alphac(lambda to infinity) approximately= 1.07. As alpha decreases below alpha0(lambda) the FM retrieval states become ground states of the system, where alpha0(0) = 0.05 and alpha0(lambda to infinity) = 2/pi.