A characterization of the existence of energies for neural networks

  • Michel Cosnard
  • Eric Goles
Learning, Coding, Robotics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 944)


In this paper we give under an appropriate theoretical frame-work a characterization about neural networks which admit an energy. We prove that a neural network 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fogelman-Soulié, F., Goles, E., Weisbuch, G.: Transient length in sequential iteration of threshold functions. Disc. Appl. Math. 6, (1983) 95–98Google Scholar
  2. 2.
    Goles, E., Fogelman-Soulié, F., Pellegrin, D.: Decreasing energy functions as a tool for studying threshold netwoks. Disc. Appl. Math. 12, (1985) 261–277Google Scholar
  3. 3.
    Goles, E., Martinez, S.: Neural and automata networks. Math. and Applications, 58, Kluwer Acad. Pub., (1990)Google Scholar
  4. 4.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci., USA, 79, (1982) 2554–2558Google Scholar
  5. 5.
    Kobuchi, Y.: State evaluation functions and Lyapunov functions for neural networks. Neural Networks, 4, (1991) 505–510Google Scholar
  6. 6.
    X. Xu W.T. Tsai, Construction associative memories using neural networks. Neural Networks, 3, (1990) 301–309Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Michel Cosnard
    • 1
    • 2
  • Eric Goles
    • 1
    • 2
  1. 1.Laboratoire de l'Informatique du ParallélismeCNRS Ecole Normale Supérieure de LyonLyonFrance
  2. 2.Departamento de Ingeniería MatemáticaUniversidad de ChileSantiagoChile

Personalised recommendations