Skip to main content
Log in

Information processing in three-state neural networks

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We introduce networks of three-state neurons, where the additional state embodies the absence of information. Their dynamical behavior is studied from the standpoint of information processing. These networks display strong pattern completion capabilities. Moreover, inference naturally occurs between coherent patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Grossberg,The Adaptive Brain, Vols. 1 and 2 (North-Holland, Amsterdam, 1987).

    Google Scholar 

  2. T. Kohonen,Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).

    Google Scholar 

  3. F. Rosenblatt,Principles of Neurodynamics (Spartan, New York, 1962).

    Google Scholar 

  4. M. Minsky and S. Papert,Perceptrons: An Introduction to Computational Geometry (MIT Press, Cambridge, Massachusetts, 1969).

    Google Scholar 

  5. S. Amari,Proc. IEEE 59:35–47 (1972).

    Google Scholar 

  6. S. Amari,Kybernetic 14:201–215 (1974).

    Google Scholar 

  7. T. Kohonen,IEEE Trans. C-21:353–359 (1972).

    Google Scholar 

  8. J. J. Hopfield,Proc. Natl. Acad. Sci. USA 79:2554–2558 (1982).

    Google Scholar 

  9. M. Mézard, G. Parisi, and M. A. Virasoro,Spin Glass Theory and Beyond (World Scientific, Singapore, 1986).

    Google Scholar 

  10. J. J. Hopfield and D. W. Tank,Biol. Cybernet. 52:147–152 (1985).

    Google Scholar 

  11. I. Morgenstern, Spin-glasses, optimization and neural networks, inProceedings of the Heidelberg Colloquium on Glassy Dynamics and Optimization; Heidelberg 1986, J. L. Van Hemmen and I. Morgenstern, eds. (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  12. W. D. Hillis,The Connection Machine (MIT Press, Cambridge, Massachusetts, 1986).

    Google Scholar 

  13. U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett. 56(14):1506–1508 (1986).

    Google Scholar 

  14. B. Kosko and C. Guest, Optical bidirectional associative memories,Proc. SPIE: Image Understanding 1987:758.

  15. D. Psaltis, D. Brady, X. Gu, and K. Hsu, Optical implementation of neural computers, inOptical Processing and Computing, H. Arsenault, ed. (Academic Press, New York, 1988).

    Google Scholar 

  16. E. Domany, R. Meir, and W. Kinzel,Europhys. Lett. 2(3):175–185 (1986).

    Google Scholar 

  17. T. J. Sejnowski and C. R. Rosenberg,Complex Syst. 1:145–168 (1987).

    Google Scholar 

  18. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Learning internal representation by error propagation, inParallel Distributed Processing: Explorations in the Microstructures of Cognition (MIT Press, Cambridge, Massachusetts, 1986).

    Google Scholar 

  19. P. Rùjan and M. Marchand, Learning by activating neurons: A new approach to learning in neural networks, Preprint Institut für Festkörperforschungsanlage der Kernforschungsanlage Jülich (1988).

  20. D. J. Amit, The properties of models of simple neural networks, inProceedings of the Heidelberg Colloquium on Glassy Dynamics and Optimization;Heidelberg 1986, J. L. Van Hemmen and I. Morgenstern, eds. (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  21. D. J. Amit, H. Gutfreund, and H. Sompolinski,Ann. Phys. (N.Y.) 173:30–67 (1987).

    Google Scholar 

  22. K. Y. M. Wong and D. Sherrington,Europhys. Lett. 7(3):197–202 (1988).

    Google Scholar 

  23. W. S. MacCulloch and W. Pitss,Bull. Math. Biophys. 5:115–133 (1943).

    Google Scholar 

  24. D. O. Hebb,The Organization of Behavior (Wiley, New York, 1949).

    Google Scholar 

  25. J. S. Denker,Physica D 22:216–232 (1986).

    Google Scholar 

  26. H. Sompolinski, The theory of neural networks: The Hebb rule and beyond, inProceedings of the Heidelberg Colloquium on Glassy Dynamics and Optimization;Heidelberg 1986, J. L. Van Hemmen and I. Morgenstern, eds. (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  27. J. L. Van Hemmen, D. Grensing, A. Huber, and R. Kühn,J. Stat. Phys. 50(1/2):231–293 (1988).

    Google Scholar 

  28. W. A. Little,Math. Biosci. 19:101 (1974).

    Google Scholar 

  29. J. F. Fontanari and R. Köberle,J. Phys. France 49:13–23 (1988).

    Google Scholar 

  30. B. Derrida, E. Gardner, and A. Zippelius,Europhys. Lett. 4(2):167–173 (1987).

    Google Scholar 

  31. W. Kinzel, Neural networks with asymmetric bonds, inProceedings of the Heidelberg Colloquium on Glassy Dynamics and Optimization;Heidelberg 1986, J. L. Van Hemmen and I. Morgenstern, eds. (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  32. G. Parisi,J. Phys. A: Math. Gen. 19:675–680 (1986).

    Google Scholar 

  33. P. Peretto,J. Phys. France 49:711–726 (1988).

    Google Scholar 

  34. A. Canning and E. Gardner, Partially connected models of neural networks,J. Phys. A, submitted.

  35. E. Gardner,J. Phys. A: Math. Gen. 21:257–270 (1988).

    Google Scholar 

  36. M. Mézard and M. A. Virosoro,J. Phys. France 46:1293–1307 (1985).

    Google Scholar 

  37. M. Mézard, J. P. Nadal, and G. Toulouse,J. Phys. France 47:1457–1462 (1986).

    Google Scholar 

  38. J. P. Nadal, G. Toulouse, J. P. Changeux, and S. Dehaene,Europhys. Lett. 1(10):535–542 (1986).

    Google Scholar 

  39. M. V. Feigelman and L. B. Ioffe,Int. J. Mod. Phys. B 1:51–68 (1987).

    Google Scholar 

  40. L. Personnaz, I. Guyon, and G. Dreyfus,J. Phys. Lett. 46:359–365 (1985).

    Google Scholar 

  41. T. Kohonen and M. Ruohonen,IEEE Trans. Comput. C22:701 (1973).

    Google Scholar 

  42. L. Personnaz, I. Guyon, and G. Dreyfus,Europhys. Lett. 4(8):863–867 (1987).

    Google Scholar 

  43. H. Gutfreund,Phys. Rev. A 37(2):570–577 (1988).

    Google Scholar 

  44. N. Parga and M. A. Virasoro,J. Phys. France 47:1857–1864 (1986).

    Google Scholar 

  45. D. J. Amit, H. Gutfreund, and H. Sompolinski,Phys. Rev. A 35(5):2293–2303 (1987).

    Google Scholar 

  46. J. J. Hopfield, D. I. Feinstein, and R. G. Palmer,Nature 304:158–159 (1983).

    Google Scholar 

  47. S. W. Kuffler and J. Nicholls,From Neuron to Brain (Sinauer Associates, Sunderland, Massachusetts, 1967).

    Google Scholar 

  48. J. Yedidia, private communication.

  49. E. Gardner,J. Phys. A: Math. Gen. 19:1047 (1986).

    Google Scholar 

  50. D. H. Ballard,Artificial Intelligence 22:235–267 (1984).

    Google Scholar 

  51. Y. Lecun, inProceedings Cognitiva 85 (CESTA-AFCET, 1985), p. 599.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meunier, C., Hansel, D. & Verga, A. Information processing in three-state neural networks. J Stat Phys 55, 859–901 (1989). https://doi.org/10.1007/BF01041070

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01041070

Key words

Navigation