Stochastic neural networks and the weighted Hebb rule

Neural networks with synaptic connections based on the weighted Hebb rule are studied in the presence of noise, in the limit when the size of the network is very large. The presence of a sufficient amount of noise, measured by a critical temperature T_c, results in the elimination of spurious local minima. It is shown that the inclusion of even a single pattern weighted sufficiently more than all the rest can result in a T_c that is lower than that for a normal Hebbian network without this extra pattern. By suitably adjusting the weights, therefore, the convergence time of the network can be reduced significantly due to the lower operating temperature; simultaneously, the overlaps of the fixed points of the network with the stored patterns are better.