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Emulation of Hopfield Networks with Spiking Neurons in Temporal Coding

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Computational Neuroscience

Abstract

A theoretical model for analog computation with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analog computations with temporal coding in networks of detailed compartmental neuron models. One arrives in this way at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different firing patterns for different inputs.

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References

  1. J. Hopfield. Pattern recognition computing using action potential timing for stimulus representation. Nature, 376: 33–36, 1995.

    Article  PubMed  CAS  Google Scholar 

  2. S. T. Thorpe and M. Imbert. Biological constraints on connectionist modelling. In R. Pfeifer, Z. Schreter, F. Fogelman-Soulie, and L. Steels, editors, Connectionism in Perspective. Elsevier, 1989.

    Google Scholar 

  3. T. W. Kjaer, T. J. Gawne, and B. J. Richmond. Latency: Another potential code for feature binding in striate cortex. Journal of Neurophysiology, 76(2): 1356–1360, 1996.

    PubMed  Google Scholar 

  4. W. Gerstner and J. L. van Hemmen. Associative memory in a network of “spiking” neurons. Network, 3: 139–164, 1992.

    Article  Google Scholar 

  5. W. Maass. Fast sigmoidal networks via spiking neurons. Neural Computation, 9: 279–304, 1997.

    Article  PubMed  CAS  Google Scholar 

  6. J. J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences, USA, 81: 3088–3092, 1984.

    Article  CAS  Google Scholar 

  7. W. Maass and T. Natschläger. Networks of spiking neurons can emulate arbitrary Hopfield networks in temporal coding. Network: Computation in Neural Systems, 8(4): 355–372, 1997.

    Article  Google Scholar 

  8. J. M. Bower and D. Beeman. The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural Simulation System. Springer-Verlag, Inc. Published by TELOS, New York, 1995.

    Google Scholar 

  9. A. Zador, H. Agmon-Snir, and I. Segev. The morphoelectronic transform: A graphical approach to dendritic function. The Journal of Neuroscience, 15(3): 1669–1682, 1995.

    PubMed  CAS  Google Scholar 

  10. Y. Manor, C. Koch, and I. Segev. Effect of geometrical irregularities on propagation delay in axonal trees. Biophysical Journal, 60: 1424–1437, 1991.

    Article  PubMed  CAS  Google Scholar 

  11. J. Hertz, A. Krogh, and R. G. Palmer. Introduction to the Theory of Neural Computation. Addison-Wesley, 1991.

    Google Scholar 

  12. E. Fransén. Biophysical Simulation of Cortical Associative Memory. PhD thesis, Stockholm University, October 1996.

    Google Scholar 

  13. M. W. Simmen, E. T. Rolls, and A. Treves. Rapid retrieval in an autoassociative network of spiking neurons. In J. M. Bower, editor, Computational Neuroscience, pages 273–278. Academic Press, London, 1995.

    Google Scholar 

  14. R. Ritz, W. Gerstner, U. Fuentes, and J. L. van Hemmen. A biologically motivated and analytically soluble model of collective oscillations in the cortex. Biological Cybernetics, 71: 349–358, 1994.

    Article  PubMed  CAS  Google Scholar 

  15. A. Lansner and E. Fransen. Modelling hebbian cell assemblies comprised of cortical neurons. Network, 3: 105–119, 1992.

    Article  Google Scholar 

  16. A. V. M. Herz, Z. Li, and J. L. van Hemmen. Statistical mechanics of temporal association in neural networks with transmission delays. Physical Review Letters, 66(10): 1370–1373, 1991.

    Article  PubMed  Google Scholar 

  17. M. Abeles. Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge University Press, 1991.

    Google Scholar 

  18. M. Abeles, H. Bergman, E. Margalit, and E. Vaadia. Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. Journal of Neurophysiologie, 70(4): 1629–1638, October 1993.

    CAS  Google Scholar 

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© 1998 Springer Science+Business Media New York

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Maass, W., Natschläger, T. (1998). Emulation of Hopfield Networks with Spiking Neurons in Temporal Coding. In: Bower, J.M. (eds) Computational Neuroscience. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4831-7_37

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  • DOI: https://doi.org/10.1007/978-1-4615-4831-7_37

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7190-8

  • Online ISBN: 978-1-4615-4831-7

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