Skip to main content
SpringerLink
Log in

Associative Memory and Its Statistical Neurodynamical Analysis

  • Conference paper
Neural and Synergetic Computers

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 42))

Abstract

A neural network is a complex system consisting of a large number of mutually connected elements having a simple input-output relation. Its behavior is highly non-linear, so that it is in general difficult to analyze its dynamical behavior of information processing. In order to elucidate a typical behavior, we study a network whose connection weights or synaptic efficacies of connections are randomly generated and then fixed. Given a probability law of connection weights, we have an ensemble of randomly generated networks. Statistical neurodynamics provides a theoretical method to search for macroscopic behaviors which are shared by all typical random networks in the ensemble, i.e. those networks generated by the same probability law.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amari, S. [ 1971 ]: “Characteristics of randomly connected threshold element networks and network systems”, Proc. IEEE, 59, 35–47.

    Article  MathSciNet  Google Scholar 

  2. Amari, S. [ 1972a ]: “Characteristics of random nets of analog neuron-like elements”, IEEE Trans., SMC-2, 643–657.

    Google Scholar 

  3. Amari, S. [ 1974 ]: “A method of statistical neurodynamics”, Kybernetik, 14, 201–215.

    MathSciNet  MATH  Google Scholar 

  4. Amari, S. Yoshida, K., and Kanatani, K. [19 7 7]: “A mathematical foundation for statistical neurodynamics”, SIAM J. App. Math., 33, 95–126.

    Article  MathSciNet  MATH  Google Scholar 

  5. Amari, S. andMaginu,K. [ 1988 ]: “Statistical neurodynamics of associative memory”, Neural Networks, 1, 63–73

    Article  Google Scholar 

  6. Nakano, K. [ 1972 ]: “Association — a model of associative memory”, IEEE Trans., SMC-2, 381–388

    Google Scholar 

  7. Kohonen, T. [ 1972 ]: “Correlation matrix memories”, IEEE Trans., C-21, 353–359.

    Google Scholar 

  8. Anderson, J. A. [ 1972 ]: “A simple neural network generating interactive memory”, Math. Biosciences, 14, 197–220.

    Google Scholar 

  9. Amari, S. [ 1972 ]: “Learning patterns and pattern sequences by self-organizing nets of threshold elements”, IEEE Trans., C-21, 1197–1206.

    MathSciNet  Google Scholar 

  10. Amari, S. [ 1977 ]: “Neural theory of association and concept-formation”, Biol. Cybernetics, 26, 175–185.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hopfield, J. J.[ 1982 ]: “Neural networks and physical systems with emergent collective computational abilities”, P. Nat. Acad. Sci. U.S.A., vol. 79, 2445–2458.

    MathSciNet  Google Scholar 

  12. Amit, D. J., Gutfreund, H. and Sompolinsky, H. [ 1986 ]: “Spin-glass models of neural networks”, Phys. Rev., A2, 1007–1018.

    MathSciNet  Google Scholar 

  13. Meir, R. and Domany, E. [ 1987 ]: “Exact solution of a layered neural network memory”, Phy. Rev. Lett., 59, 359–362.

    Article  ADS  Google Scholar 

  14. McEliece, R. J. et. al. [ 1987 ]: “The Capacity of the Hopfield associative memory”, IEEE Trans., Inf. Theory, IT-33, 461–482.

    Article  MathSciNet  Google Scholar 

  15. Kosko, B. [ 1987 ]: “Adaptive bilateral associative memory”, Appl. Oct., 26, 4947–4960.

    Article  ADS  Google Scholar 

  16. Okajima, K., Tanaka, S. and Fujiwara, S. [ 1977 ]: “A heteroassociative memory network wirh feedback connection”, Proc. 1st Int. Conf. Neural Networks, II -711–II -718.

    Google Scholar 

  17. Cottrell, M. [ 1988 ]: “Stability and attractivity in associative memory networks”, Biol. Cybern, 58, 129–139.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kinzel, W. [ 1985 ]: “Learning and pattern recognition in spin glass models”, Z. Physik, B60, 205–213.

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan

    Shun-ichi Amari

Authors
  1. Shun-ichi Amari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57/IV, D-7000, Stuttgart 80, Fed. Rep. of Germany

    Hermann Haken

  2. Center for Complex Systems, Florida Atlantic University, 33431, Boca Raton, FL, USA

    Hermann Haken

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Amari, Si. (1988). Associative Memory and Its Statistical Neurodynamical Analysis. In: Haken, H. (eds) Neural and Synergetic Computers. Springer Series in Synergetics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74119-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-74119-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74121-0

  • Online ISBN: 978-3-642-74119-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation