title: Topological pattern selection in recurrent networks.
abstract: The impact of adding correlation to a population of neurons on the information and the activity of the population is one of the fundamental questions in recent system neuroscience. In this paper, we would like to introduce topology-based correlation at the level of storing patterns in a recurrent network. We then study the effects of topological patterns on the activity and memory capacity of the network. The general aim of the present work is to show how the repertoire of possible stored patterns is determined by the underlying network topology. Two topological probability rules for pattern selection in recurrent network are introduced. The first one selects patterns according to a Gibbs-type distribution. We start with a Hopfield-type dynamics on a ring model and then a Langevin model on a general random graph is treated. The phenomenon of phase transition in pattern selection motivated us to introduce an alternative topological rule for pattern selection. In a network of N neurons on a random d-regular graph, two asymptotic cases, d/N→0 and d/N→1, have been discussed for the new rule, and it is shown that capacity of the network grows considerably as d/N→1. By introducing the notions of asymptotic eigenvector, we will be able to study the behaviour of the discrete model in the limit d/N→0. It will be proved that for degree d less than a critical value there is a positive role for noise, in which case increasing the number of patterns will improve the storage capacity.
authors.affiliation: Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran. bahraini@sharif.ir
authors.forename: Alireza
authors.initials: A
authors.lastname: Bahraini
authors.forename: Abdolhossein
authors.initials: A
authors.lastname: Abbassian
mesh_terms: D016571:Neural Networks, Computer; D009474:Neurons; D011897:Random Allocation; D059629:Signal-To-Noise Ratio; D013997:Time Factors