The interaction space of neural networks with sign-constrained synapses

Abstract

The authors investigate the optimal storage capacity of attractor neural networks with sign-constrained weights, which are prescribed a priori. The storage capacity is calculated by considering the fractional volume of weights which can store a set of random patterns as attractors, for a given stability parameter. It is found that this volume is independent of the particular distribution of signs (gauge invariance) and that the storage capacity of such constrained networks is exactly one half that of the unconstrained network with the corresponding value of the stability parameter.