Searching real-valued synaptic weights of Hopfield's associative memory using evolutionary programming

  • Akira Imada
  • Keijiro Araki
Evolutionary Methods for Modeling and Training
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1213)


We apply evolutionary computations to Hopfield model of associative memory. Although there have been a lot of researches which apply evolutionary techniques to layered neural networks, their applications to Hopfield neural networks remain few so far. Previously we reported that a genetic algorithm using discrete encoding chromosomes evolves the Hebb-rule associative memory to enhance its storage capacity. We also reported that the genetic algorithm evolves a network with random synaptic weights eventually to store some number of patterns as fixed points. In this paper we present an evolution of the Hopfield model of associative memory using evolutionary programming as a real-valued parameter optimization.


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  1. 1.
    J. Komlós, and R. Paturi (1988) “Convergence Results in an Associative Memory Model.” Neural Networks 1, pp239–250.CrossRefGoogle Scholar
  2. 2.
    J. J. Hopfield (1982) “Neural Networks and Physical Systems with Emergent Collective Computational Abilities.”, Proceedings of the National Academy of Sciences, USA, 79, pp2554–2558.Google Scholar
  3. 3.
    D. O. Hebb (1949) The Organization of Behavior., Wiley.Google Scholar
  4. 4.
    D. J. Amit, H. Gutfreund, and H. Sompolinsky (1985) “Storing Infinite Number of Patterns in a Spin-glass Model of Neural Networks.” Physical Review Letters 55, pp1530–1533.CrossRefPubMedGoogle Scholar
  5. 5.
    R. J. McEliece, E. C. Posner, E. R. Rodemick, and S. S. Venkatesh (1987) “The Capacity of the Hofpield Associative Memory.” IEEE Trans. Information Theory IT-33, pp461–482.CrossRefGoogle Scholar
  6. 6.
    T. Kohonen, and M. Ruohonen (1973) “Representation of Associated Data by Matrix Operators.” IEEE Trans. Computers C-22(7), pp701–702.Google Scholar
  7. 7.
    G. Pancha, S. S. VenKatesh (1993) “Feature and Memory-Selective Error correction in Neural Associative Memory.” in M. H. Hassoun eds. Associative Neural Memories: Theory and Implementation, Oxford University Press, p225–248.Google Scholar
  8. 8.
    B. Derrida, E. Gardner, and A. Zippelius (1987) “An Exactly Soluble Asymmetric Neural Network Model.” Europhys. Lett. 4, pp167–173.Google Scholar
  9. 9.
    A. Imada, and K. Araki (1995) “Mutually Connected Neural Network Can Learn Some Patterns by Means of GA.”, Proceedings of the World Congress on Neural Networks, vol. 1, pp803–806.Google Scholar
  10. 10.
    J. Holland (1975) Adaptation in Natural and Artificial Systems. The University of Michigan PressGoogle Scholar
  11. 11.
    A. Imada, and K. Araki (1995) “Genetic Algorithm Enlarges the Capacity of Associative Memory.”, Proceedings of 6th International Conference on Genetic Algorithms, pp413–420.Google Scholar
  12. 12.
    E. Gardner (1988) “The Phase Space of Interactions in Neural Network Models” J. Phys 21A, pp257–270.Google Scholar
  13. 13.
    T. D. Chiueh, and R. M. Goodman (1991) “Recurrent Correlation Associative Memories.” IEEE Trans. Neural Networks 2(2), pp275–284.CrossRefGoogle Scholar
  14. 14.
    H. Sompolinsky (1986) Neural Network with Non-linear Synapses and Static Noise Phys. Rev. A34 pp2571–2574Google Scholar
  15. 15.
    D. B. Fogel (1992) “An Analysis of Evolutionary Programming.” Proceedings of 1st Annual Conference on Evolutionary Programming, pp43–51.Google Scholar
  16. 16.
    J. A. Hertz, G. Grinstein, and S. A. Solla (1987) “Irreversible Spin Glasses an Neural Networks.” in L. N. van Hemmen and I. Morgenstern eds. Heidelberg Colloquium on Glassy Dynamics. Lecture Notes in Physics 275 Springer-Verlag, pp538–546.Google Scholar
  17. 17.
    G. Parisi (1986) “Asymmetric Neural Networks and the Process of Learning.” J. Phys. A19, ppL675–L680.MathSciNetGoogle Scholar
  18. 18.
    W. Krauth, J.-P. Nadal, and M. Mezard (1988) The Roles of Stability and Symmetry in the Dynamics of Neural Networks, J. Phys. A: Math. Gen. 21, pp2995–3011.CrossRefGoogle Scholar
  19. 19.
    M. Verleysen, J.-D. Legat, and P. Jespers (1993) Analog implementation of an Associative Memory: Learning Algorithm and VLSI Constraints. in M. H. Hassoun eds Associative Neural Memories: Theory and Implementation, Oxford University Press, pp265–275.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Akira Imada
    • 1
  • Keijiro Araki
    • 2
  1. 1.Graduate School of Information ScienceNara Institute of Science and TechnologyNaraJapan
  2. 2.Department of Computer Science and Computer Engineering Graduate School of Information Science and Electrical EngineeringKyusyu UniversityFukuokaJapan

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