Discrete time leaky integrator network with synaptic noise

Abstract

A dynamical model of a binary neural network is developed which incorporates certain important neurophysiological features of real neurons missing from most artificial network models. This is achieved by constructing a discrete time approximation of a leaky integrator model with synaptic noise and shunting inhibition. The associated dynamical equations describe a network of stochastic binary neurons with extended time summation and thresholding activity which is nonlinear in weights. The weights and thresholds are random variables independently updated at every time step from fixed probability distributions. An extension to the case of multicompartmental models is also considered. Finally, the stochastic dynamics of discrete time leaky integrator networks is analysed and a comparison is made with the Hopfield-Little model, which may be obtained from the former as a limiting case.