Stochastic Dynamics of Neural Networks

The dynamics of stochastic neural networks are presented. The model is an algorithm based upon the assumption that the activities of neurons are asynchronous. It is proven that networks with fixed synaptic efficacies cannot sustain oscillating activities. Following Choi and Huberman, the dynamics of instantaneous frequencies is derived. The equations are solved for associative and for recursive networks by introducing order parameters coupled to stored patterns. It is shown that the networks relax towards one of the stored configurations in a matter of a few refractory periods, whatever the size of the network. The relaxation time diverges in recursive networks at a critical noise Bc, above which no stored pattern can be retrieved. These results have been confirmed using computer simulations.