Skip to main content

Can a Niching Method Locate Multiple Attractors Embedded in the Hopfield Network?

  • Conference paper
  • First Online:
Simulated Evolution and Learning (SEAL 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1585))

Included in the following conference series:

  • 949 Accesses

Abstract

We apply evolutionary computations to the Hopfield’s neural network model of associative memory. In the model, a number of patterns can be stored in the network as attractors if synaptic weights are determined appropriately. So far, we have explored weight space to search for the optimal weight configuration that creates attractors at the location of patterns to be stored. In this paper, on the other hand, we explore pattern space to search for attractors that are created by a fixed weight configuration. All the solutions in this case are a priori known. The purpose of this paper is to study the ability of a niching genetic algorithm to locate these multiple solutions using the Hopfield model as a test function.

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

Access this chapter

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.

Similar content being viewed by others

References

  • Amit, D. J. (1989) Modeling Brain Function: The World of Attractor Neural Networks. Cambridge University Press.

    Google Scholar 

  • Davis, L (1991) Bit-Climbing, Representation Bias, and Test Suite Design. Proceedings of the 4th International Conference on Genetic Algorithms, pp.18–23.

    Google Scholar 

  • De Jong, K. A. (1975) An Analysis of the Behavior of a Class of Genetic Adaptive Systems. Ph.D. theses University of Michigan.

    Google Scholar 

  • Gardner, E. (1988) The Phase Space of Interactions in Neural Network Models. Journal of Physics, 21A, pp257–270.

    Google Scholar 

  • Goldberg, D. E., and J. Richardson (1987) Genetic Algorithms with Sharing for Multimodal function Optimization. Proceedings of 2nd International Conference on Genetic Algorithms, pp.41–49.

    Google Scholar 

  • Hebb, D. O. (1949) The Organization of Behavior. Wiley.

    Google Scholar 

  • Holland, J. (1975) Adaptation in Natural and Artificial Systems. The University of Michigan Press.

    Google Scholar 

  • Hopfield, J. J. (1982) Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings of the National Academy of Sciences, USA, 79, pp2554–2558.

    Article  MathSciNet  Google Scholar 

  • Imada, A., and K. Araki (1997a), Random Perturbations to Hebbian Synapses of Associative Memory using a Genetic Algorithm. Proceedings of International Work-Conference on Artificial and Natural Neural Networks. Springer Verlag, Lecture Notes in Computer Science, No.1240, pp398–407.

    Google Scholar 

  • Imada, A., and K. Araki (1997b) Evolution of Hopfield Model of Associative Memory by the Breeder Genetic Algorithm. Proceedings of the 7th International Conference on Genetic Algorithms, pp784–791.

    Google Scholar 

  • Komlós, J., and R. Paturi (1988) Convergence Results in an Associative Memory Model. Neural Networks 1, pp239–250.

    Article  Google Scholar 

  • Mahfoud, S. W. (1992) A Comparison of Parallel and Sequential Niching Methods. Proceedings of the 2nd Parallel Problem Solving from Nature, pp.27–36.

    Google Scholar 

  • Mahfoud, S. W. (1995) A Comparison of Parallel and Sequential Niching Methods. Proceedings of the 6th International Conference on Genetic Algorithms, pp.136–143.

    Google Scholar 

  • Mattis, D. C. (1976) Solvable Spin Systems with Random Interactions. Physics Letters, 56A, pp421–422.

    Google Scholar 

  • Sherrington, D., and S. Kirkpatrick (1975) Solvable Model of a Spin Glass. Physical Review Letters 35, pp1792–1796.

    Article  Google Scholar 

  • Syswerda, G. (1989) Uniform Crossover in Genetic Algorithms. Proceedings of the 3rd International Conference on Genetic Algorithms, pp2–9.

    Google Scholar 

  • Whitley, D., K. Mathias, S. Rana, and J. Dzubera (1995) Building Better Test Functions. Proceedings of the 6th International Conference on Genetic Algorithms, pp239–246.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Imada, A., Araki, K. (1999). Can a Niching Method Locate Multiple Attractors Embedded in the Hopfield Network?. In: McKay, B., Yao, X., Newton, C.S., Kim, JH., Furuhashi, T. (eds) Simulated Evolution and Learning. SEAL 1998. Lecture Notes in Computer Science(), vol 1585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48873-1_42

Download citation

  • DOI: https://doi.org/10.1007/3-540-48873-1_42

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65907-5

  • Online ISBN: 978-3-540-48873-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics