title: Discrete State Neural Networks and Energies.
abstract: In this paper we give under an appropriate theoretical framework a characterization about neural networks (evolving in a binary set of states) which admit an energy. We prove that a neural network, iterated sequentially, admits an energy if and only if the weight matrix verifies two conditions: the diagonal elements are non-negative and the associated incidence graph does not admit non-quasi-symmetric circuits. In this situation 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 incidence graph does not contain non-quasi-symmetric circuits. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.
authors.affiliation: Universidad de Chile, Chile
authors.forename: Eric
authors.initials: E
authors.lastname: Goles
authors.forename: Michel
authors.initials: M
authors.lastname: Cosnard