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Transient dynamics of sparsely connected Hopfield neural networks with arbitrary degree distributions

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  • Zhang, Pan
  • Chen, Yong

Abstract

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As illustrative examples, the explicit calculations of dynamics for networks with binomial, power-law, and uniform degree distribution are performed. The results are good agreement with the extensive numerical simulations. It indicates that with the same average degree, there is a gradual improvement of network performance with increasing sharpness of its degree distribution, and the most efficient degree distribution for global storage of patterns is the delta function.

Suggested Citation

  • Zhang, Pan & Chen, Yong, 2008. "Transient dynamics of sparsely connected Hopfield neural networks with arbitrary degree distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 1009-1015.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:4:p:1009-1015
    DOI: 10.1016/j.physa.2007.09.047
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    References listed on IDEAS

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    1. Theumann, W.K., 2003. "Mean-field dynamics of sequence processing neural networks with finite connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 1-12.
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