STATISTICAL-MECHANICS OF TEMPORAL ASSOCIATION IN NEURAL NETWORKS WITH TRANSMISSION DELAYS

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the deterministic dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations.