Skip to main content
SpringerLink
Log in

Associative Memories in Infinite Dimensional Spaces

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

A generalization of the Little–Hopfield neural network model for associative memories is presented that considers the case of a continuum of processing units. The state space corresponds to an infinite dimensional euclidean space. A dynamics is proposed that minimizes an energy functional that is a natural extension of the discrete case. The case in which the synaptic weight operator is defined through the autocorrelation rule (Hebb rule) with orthogonal memories is analyzed. We also consider the case of memories that are not orthogonal. Finally, we discuss the generalization of the non deterministic, finite temperature dynamics.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Little, W. A.: The existence of persistent states in the brain, Math. Biosci. 19 (1974), 101–120.

    Google Scholar 

  2. Little, W. A.: Analytic study of the memory storage capacity of a neural network, Math. Biosci. 39 (1978), 281–290.

    Google Scholar 

  3. Hebb, D. O.: The Organization of Behavior: A Neuropsychological Theory, New York, Wiley, 1949.

    Google Scholar 

  4. Amit, D. J.: Modeling Brain Function, Cambridge, Cambridge University Press, 1989.

    Google Scholar 

  5. Hopfield, J. J.: Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. 79 (1982), 2554–2558.

    Google Scholar 

  6. Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. 81 (1984), 3088–3092.

    Google Scholar 

  7. Feynman, R. P. and Hibbs, A. R.: Quantum Mechanics and Path Integrals, New York, McGraw-Hill, 1965.

    Google Scholar 

  8. Fodor, J. A.: The Modularity of Mind, Cambridge, MIT Press, 1983.

    Google Scholar 

  9. Van Kampen, N. G.: Stochastic Processes in Physics and Chemistry, Amsterdam, Elsevier, 1997.

    Google Scholar 

  10. Hinton, G. E. and Sejnowsky, T. J.: Optimal perceptual inference, In: Proc. IEEE Conf. Computer Vision and Pattern Recognition (Washington, 1983), New York, IEEE, 1983, pp. 448–453.

    Google Scholar 

  11. Peretto, P.: Collective properties of neural networks: A statistical physics approach, Biological Cybernetics 50, 51–62.

  12. Glauber, R. J.: Time dependent statistics of the Ising model, J. of Math. Phys. 4 (1963), 294–307.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Computacion, Universidad de Buenos Aires, Pabellon I Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Enrique Carlos Segura

  2. Centro de Estudios Avanzados, Universidad de Buenos Aires, Argentina

    Roberto P. J. Perazzo

Authors
  1. Enrique Carlos Segura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto P. J. Perazzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Segura, E.C., Perazzo, R.P.J. Associative Memories in Infinite Dimensional Spaces. Neural Processing Letters 12, 129–144 (2000). https://doi.org/10.1023/A:1009689025427

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009689025427

Search

Navigation