Discete state neural networks and energies

Michel Cosnard, Eric Goles

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish
Pages (from-to)327-334
Number of pages8
JournalNeural Networks
Issue number2
StatePublished - Mar 1997


  • Hopfield networks
  • direct graphs
  • energy
  • parallel update
  • quasi-symmetric weights
  • sequential update
  • symmetric weights


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