DISCRETE STATE NEURAL NETWORKS AND ENERGIES

In this paper we give under an appropriate theoretical framework a cha racterization about neural networks (evolving in a binary set of state s) which admit an energy. We prove that a neural network, iterated seq uentially, admits an energy if and only if the weight verifies two con ditions: the diagonal elements are non-negative and the associated inc idence graph does not admit non-quasi-symmetric circuits. In this situ ation the dynamics are robust with respect to a class of small changes of the weight matrix. Further, for the parallel update we prove that a necessary and sufficient condition to admit an energy is that the in cidence graph does not contain non-quasi-symmetric circuits. (C) 1997 Elsevier Science Ltd. All Rights Reserved.