Stochastic Hopfield neural networks

Hopfield (1984 Proc. Natl Acad. Sci. USA 81 3088–92) showed that the time evolution of a symmetric neural network is a motion in state space that seeks out minima in the system energy (i.e. the limit set of the system). In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the system still approaches some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic neural network will approach its limit set.