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Hopfield network with directed bonds

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Zeitschrift für Physik B Condensed Matter

Abstract

The Hopfield model for neural networks is extended to the case of directed connections. Numerical simulations show that for deterministic dynamics the model has a sharp overloading transition at a critical concentration of patterns, α c =0.0078±0.001. Distribution of overlaps and cycle lengths are calculated and discussed. The basins of attraction are compared with the ones of the symmetrical model.

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References

  1. For an introduction see: Kinzel, W.: In: Complex systemsoperational approaches. Haken, H. (ed.). Berlin, Heidelberg, New York: Springer 1985; Phys. Scr.35, 398 (1987); Amit, D., Sompolinsky, H.: In: Heidelberg Colloquium on Glassy Dynamics. In: Lecture Notes in Physics. Hemmen, J.L. van, Morgenstern, I. (eds.), Vol. 275, pp. 430, 485. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  2. Hopfield, J.J.: Proc. Natl. Acad. Sci. (USA)79, 2554 (1982)

    Google Scholar 

  3. A recent review of spin glasses is: Binder, K., Young, A.P.: Rev. Mod. Phys.58, 801 (1986)

    Google Scholar 

  4. Amit, D.J., Gutfreund, H., Sompolinsky, H.: Ann. Phys.173, 30 (1987)

    Google Scholar 

  5. Peretto, P.: Biol. Cybern.50, 51 (1984)

    Google Scholar 

  6. Wolfram, S.: Theory and applications of cellular automata. Singapore: World Scientific 1986

    Google Scholar 

  7. Kauffmann, S.A.: Physica10D, 145 (1984); Derrida, B., Stauffer, D.: Europhys. Lett.2, 739 (1986); Derrida, B., Pomeau, Y.: Europhys. Lett.1, 45 (1986)

    Google Scholar 

  8. Hertz, J.A., Grinstein, G., Solla, S.A.: In: Heidelberg Colloquium on Glassy Dynamics. In: Lecture Notes in Physics. Hemmen, J.L. van, Morgenstern, I. (eds.), Vol. 275, p. 538. Berlin, Heidelberg, New York: Springer 1987; Bausch, R., Janssen, H.K., Kree, R., Zippelius, A.: J. Phys.C 19, L 779 (1986); Crisanti, A., Sompolinsky, H.: Phys. Rev.A 36, 4922 (1987); Rieger, H., Schreckenberg, M., Zittartz, J.: J. Phys.A 21, L 263 (1988)

    Google Scholar 

  9. Domany, E., Meir, R., Kinzel, W.: Europhys. Lett.2, 175 (1986); Meir, R., Domany, E.: Phys. Rev. Lett.59, 359 (1987); Phys. Rev.A 37, 608 (1988)

    Google Scholar 

  10. Derrida, B., Gardner, E., Zippelius, A.: Europhys. Lett.4, 167 (1987); Kree, R., Zippelius, A.: (to be published); Derrida, B., Nadal, J.P.: J. Stat. Phys.49, 993 (1987); Opper, M., Kleinz, J., Kinzel, W.: (to be published)

    Google Scholar 

  11. Part of the results have already been reported by Kinzel, W. at the Heidelberg Colloquium on Glassy Dynamics. In: Lecture Notes in Physics. Hemmen, L. van, Morgenstern, I. (eds.), Vol. 275, p. 529. Berlin, Heidelberg, New York: Springer 1987. Similar results have been obtained independently by Gutfreund, H., Stein, Y.: (unpublished)

    Google Scholar 

  12. McCulloch, W.S., Pitts, W.A.: Bull. Math. Biophys.5, 115 (1943)

    Google Scholar 

  13. Henkel, R.D., Kinzel, W.: J. Phys.A 20, L727 (1987)

    Google Scholar 

  14. Kohonen, T.: Self organization and associative memory. Berlin: Springer 1988.

    Google Scholar 

  15. Kinzel, W.: Z. Phys. B—Condensed Matter60, 205 (1985);62, 267 (1986)

    Google Scholar 

  16. Bruce, A.D., Gardner, E.J., Wallace, D.J.: J. Phys.A 20, 2909 (1987)

    Google Scholar 

  17. Crisanti, A., Amit, D.J., Gutfreund, H.: Europhys. Lett2, 337 (1986)

    Google Scholar 

  18. Personnaz, L., Guyon, I., Dreyfus, G.: Phys. Rev.A 34, 4217 (1986); Diederich, S., Opper, M.: Phys. Rev. Lett.58, 949 (1987)

    Google Scholar 

  19. Gardner, E.: Europhys. Lett.4, 481 (1987); Krauth, W., Mezard, M.: J. Phys.A 20, L 745 (1987)

    Google Scholar 

  20. Kinzel, W.: Phys. Rev.B 33, 5086 (1986)

    Google Scholar 

  21. Binder, K.: In: Advances on phase transitions and disorder phenomena. Busiello, G. (ed.). Singapore: World Scientific 1987

    Google Scholar 

  22. Forrest, B.M.: J. Phys.A 21, 245 (1988)

    Google Scholar 

  23. Sompolinsky, H.: Phys. Rev.A 34, 2571 (1986)

    Google Scholar 

  24. Peretto, P., Niez, J.J.: In: Disordered systems and biological organization. Bienenstock, E. (ed.). Berlin, Heidelberg, New York: Springer 1986; Sompolinsky, H., Kanter, I.: Phys. Rev. Lett.57, 2861 (1986)

    Google Scholar 

  25. Parisi, G.: J. Phys.A 19, L 675 (1986)

    Google Scholar 

  26. Treves, A., Amit, D.J.: J. Phys.A 21, 3155 (1988)

    Google Scholar 

  27. Krauth, W., Nadal, J.P., Mezard, M.: J. Phys.A 21, 2995 (1988)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Festkörperforschung der Kernforschungsanlage Jülich, Federal Republic of Germany

    P. Spitzner & W. Kinzel

  2. Institut für Theoretische Physik III der Justus-Liebig-Universität, Heinrich-Buff-Ring 16, D-6300, Giessen, Federal Republic of Germany

    P. Spitzner & W. Kinzel

Authors
  1. P. Spitzner
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  2. W. Kinzel
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Spitzner, P., Kinzel, W. Hopfield network with directed bonds. Z. Physik B - Condensed Matter 74, 539–545 (1989). https://doi.org/10.1007/BF01311400

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  • DOI: https://doi.org/10.1007/BF01311400

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