Retrieval Properties of Attractor Neural Networks Incorporating Biological Features — A Self-Consistent Signal-to-Noise Analysis

Abstract

A network of integrate-and-fire excitatory neurons is investigated using the recently proposed self-consistent signal-to-noise analysis, which provides a new method for analyzing the behaviour of networks of neurons that have asymmetric synaptic matrices. The neural dynamics is described in terms of two continuous variables, namely the firing rate and the afferent current of each (excitatory) neuron. The afferent current is described by a differential equation that includes a decay term, the weighted inputs from other excitatory neurons, and a term that models the inhibitory interneurons. The effective inhibition chosen here depends upon both the level of activity of the excitatory neurons and the stored patterns, and it serves to control the activity of the excitatory neurons through a feedback process. The afferent current induces a spike rate described by the integrate-and-fire gain function with noise, thus providing a closed set of dynamical current-rate equations. Retrieval of a memory is characterized by the set of neurons associated with the retrieved pattern firing at a substantially higher rate than the remaining quiescent neurons for some macroscopic time. The quality of retrieval of the memory is characterized by the similarity of the evoked firing rates to the stored pattern.