Statistical properties of the neuron active potential at stable states in Hopfield model

This article investigates the statistical properties of Hopfield model at its spurious stable states (SSS) and nonspurious stable states(N-SSS). It has been shown that, in Hopfield model, some stable states are learned patterns and the others are not. A stable state is spurious if it is not a learned pattern or it is nonspurious. In this article, by means of statistical neurodynamics, the probability distributions of the neuron active potential (NAP) at N-SSS and SSS are given, and the first moments and second moments of the absolute NAP are estimated. In Hopfield model, the NAP at SSS and N-SSS have almost the same distribution curves. The difference between the first moments at SSS and N-SSS is small. But the difference between the second moments is large. The statistical results of computer simulation on the NAP are consistent with the analysis results. The results can be used to improve the convergent property of Hopfield model and to design a parallel discrimination method to detect whether a recalling output is SSS or not. This method is real-time and need not refer to the learned patterns