Memory capacity in neural networks with spatial correlations between attractors

We consider the neural network model (Miyashita, 1988. Griniasty et al., 19 93) proposed to describe neurophysiological experiments in which structural ly uncorrelated patterns are converted into spatially correlated attractors . For such a network of N neurons and for values of the coupling constant a between succeeding patterns, taken in the interval [0, 1/2), we prove the existence of a threshold storage capacity alpha(c)(a) such that there exist s a local minima (in the energy function) near each of the M(N) (<alpha(c)( a)N) stimuli patterns. (C) 1999 Elsevier Science B.V. All rights reserved.