Some properties for improved information storage and retrieval in Hopfield-type neural networks

In the paper, results concerning properties of a class of Hopfield-type neural networks which can improve the information storage and retrieval of these networks are established. Under certain constraints on the diagonal elements of the connection matrix, a neural network will have only bipolar stable memory vectors; in addition, every corner of the hypercube which is in the immediate neighborhood of a stable memory vector cannot become a stable memory and is very likely to be in the domain of attraction of that stable memory vector. A new synthesis approach is also developed for associative memories which can be used to synthesize neural networks with the desired constraints. The design (synthesis) problem of feedback neural networks for associative memories is formulated as a set of linear inequalities and is solved using the perceptron training algorithm. The perceptron training in the synthesis algorithm is guaranteed to converge for the design of neural networks. To demonstrate the applicability of the present results and to compare the present synthesis approach with existing design methods, an example is considered