An associative network with spatially organized connectivity

TL;DR

This paper studies a spatially organized autoassociative neural network with asymmetric connectivity, analyzing its stability, storage capacity, and activity profiles using adapted signal-to-noise methods and simulations.

Contribution

It introduces a novel analytical approach for spatially structured networks, extending capacity calculations to arbitrary connectivity degrees.

Findings

Stable, spatially non-uniform activity profiles can emerge.

Storage capacity remains high with short-range connectivity.

Exact capacity calculations are possible for diluted random networks.

Abstract

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.