The effect of the dimensionality of interconnections on the storage capacity of a threshold controlled neural network

Abstract

The author investigates the effect of the dimensionality of the interconnections in a Hopfield-type network on the storage capacity of the network. The analysis is performed for 1D, 2D, 3D and 4D interconnection geometries. The capacity was found to be independent of the dimensionality of the interconnections 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.<>