Learning of Associative Memory Networks by Pena ty Methods

Abstract- This paper concerns the learning of asso-ciative memory networks. We derive inequality associa-tive conditions for stored patterns in the network. Un-der these associative conditions, we find regions each of which is mapped by the network function into a neigh-bor of an associative pattern. To make large the re-gions, a functional is derived using their shape. The functional is minimized under the inequality associative conditions. We show that this minimization problem has a unique solution, and solve the problem by combining the penalty methods with the gradient methods. This solving process gives a learning algorithm for associative networks. Our theory is first used to analyze two-layer autoassociative networks. I t is shown that the network function becomes a contraction mapping in each of th