The role of dimensionality in a threshold-controlled neural network

Abstract

When a network is not fully interconnected, the topology of the interconnection scheme becomes potentially important. I have investigated the effect of the dimensionality of the interconnection in a Hopfield-type network on the storage capacity of the network. The capacity was found to be independent of the dimensionality of the interconnections for 1,2,3 and 4-dimensional geometries and to depend only on the total number of interconnections available in a given network. In addition, no evidence of any instabilities was observed, in contrast to physical systems of reduced dimensionality. © 1991 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted.