Collective Computation, Content-Adressable Memory, and Optimization Problems

  • J. J. Hopfield
Chapter

Abstract

A collective decision network is described which can function as a computational element in a digital computer or signal processor. It differs from conventional digital circuit designs in emphasizing the large connectivity and analog response that biological “computational” systems employ. When such circuits have symmetric connections, they display a dynamics which is complex enough to use for computation, but simple enough to yield some general theorems about the dynamics of the circuits. Associative memory and error correcting codes are both computations which fit naturally onto the network dynamics. A large class of computational problems describable as optimizations can be mapped onto such networks. While the networks can be used to make binary decisions, during the decision process they transit the interior of a logical space of which only the boundaries have defined logical meaning.

Keywords

Associative Memory Stable Point Code Word Information Space Biological Neuron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    G.E. Hinton and J.A. Anderson, eds., Parallel Models of Associative Memory, Lawrence Erlbaum Assoaciates, Hillside, NJ (1981).Google Scholar
  2. 2.
    J.J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).MathSciNetCrossRefGoogle Scholar
  3. 3.
    G.E. Hinton and T.J. Sejnowski, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,448 (1983).Google Scholar
  4. 4.
    D.J. Amit,, H. Gutfreund, and H. Sompolinsky, Phys. Rev. Lett. 55, 1530, (1985).CrossRefGoogle Scholar
  5. 5.
    R.J. McEliece and E. C. Posner (preprint).Google Scholar
  6. 6.
    Y. S. Abu-Mostafa and J. St. Jacques, International Symposium on Information Theory(Abstracts) IEEE Catalog No. 85 CH 2201-2, 74 (1985).Google Scholar
  7. 7.
    J. Lambe, A. Moopenn, and A. P. Thakoor, Am. Inst. of Aeronautics and Astronautics, 85-5007,160(1985).Google Scholar
  8. 8.
    D. J. Willshaw, Models of Distributed Associated Memory (thesis ), Univ. of Edinburgh (1971).Google Scholar
  9. 9.
    A. E. Gelperin, J.J. Hopfield, and D.W. Tank, in Model Neural Networks and Behavior, A. Selverston, ed., Plenum Press, New York (1985).Google Scholar
  10. 10.
    J. J. Hopfield, Proc. Natl. Acad. Sci. USA, 81, 3088 (1984).CrossRefGoogle Scholar
  11. 11.
    J.J. Hopfield and D.W. Tank, Biol Cybernetics 52, 141 (1985).MathSciNetMATHGoogle Scholar
  12. 12.
    J. Lambe, A. P. Thakor, and A. Moopen, JPL Technical Report D-2825, Jet Propulsion Laboratory, Caltech, Pasadena, CA (1985).Google Scholar
  13. 13.
    D. Psaltis and N. Farhat, Optics Letters 10, 98 (1985).CrossRefGoogle Scholar
  14. 14.
    M. Sivilotti, M. Emmerling, and C.A. Mead, 1985 Conference on Very Large Scale Integration, H. Fuchs, ed., Computer Science Press, Rockville, MD (1985), p. 329.Google Scholar
  15. 15.
    L.D, Jackel, R.E. Howard, H.P. Graf, B. Straughn, and J.S. Denker, J. Vac. Sci. Tech. (in press).Google Scholar
  16. 16.
    F. Tanaka and S.F. Edwards,J. Physics F. Metal Phys. 10, 2769 (1980); G. Toulouse, Helv. Phys. Acta, 57, 459 (1984); P. Peretto, Biol. Cybernetics 50,51 (1984)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • J. J. Hopfield
    • 1
    • 2
  1. 1.Divisions of Chemistry and BiologyCalifornia Institute of TechnologyPasadenaUSA
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

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