Stochastic Neural Networks with the Weighted Hebb Rule
Caren Marzban, Raju Viswanathan · 1994
Neural networks with synaptic weights constructed according to the weighted Hebb rule are studied in the presence of noise (finite temperature), when the number of stored patterns is finite. Although, for arbitrary weights not all of the stored patterns are global minima, there exists a temperature range in which only the stored patterns are minima of the free energy. In particular, a detailed analysis reveals that in the presence of a single extra pattern stored with an appropriate weight in the synaptic rule, the temperature at which the spurious minima of the free energy are eliminated is significantly lower than for a similar network without this extra pattern. The convergence time of the network, together with the overlaps of the equilibria of the network with the stored patterns, can thereby be improved considerably. 1 Introduction The statistical mechanics of large neural networks with the Hebb rule prescription for the synaptic weights has been studied in detail and is now w...