Storage of sets of correlated data in neural network memories

Abstract

In most applications of neural network models one has to consider sets of correlated data. The authors study the problem of the storage of associated patterns in neural network memories. They consider two basic types of correlation: 'semantic' ones-among the different patterns-and 'spatial' ones-among the different sites of the network. They apply Gardner's program to evaluate optimal storage conditions for both kinds of correlation. The 'spatial' ones worsen, generally speaking, the storage properties of a simple perceptron, while they improve them for the Hopfield network. In the case of 'semantic' correlations they obtain bounds of the critical capacity for both kinds of networks; the storage ratio of the perceptron may be significantly increased in this case.