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Continuous attractors of discrete-time recurrent neural networks

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Abstract

This paper studies the continuous attractors of discrete-time recurrent neural networks. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. Continuous attractors of neural networks have been used to store and manipulate continuous stimuli for animals. A continuous attractor is defined as a connected set of stable equilibrium points. It forms a lower dimensional manifold in the original state space. Under some conditions, the complete analytical expressions for the continuous attractors of discrete-time linear recurrent neural networks as well as discrete-time linear-threshold recurrent neural networks are derived. Examples are employed to illustrate the theory.

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Authors and Affiliations

  1. Institute for Infocomm Research, Agency for Science Technology and Research, Singapore, 138632, Singapore

    Jiali Yu, Huajin Tang & Haizhou Li

  2. School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW, Australia

    Haizhou Li

Authors
  1. Jiali Yu
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  2. Huajin Tang
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  3. Haizhou Li
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Correspondence to Jiali Yu.

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Yu, J., Tang, H. & Li, H. Continuous attractors of discrete-time recurrent neural networks. Neural Comput & Applic 23, 89–96 (2013). https://doi.org/10.1007/s00521-012-0975-5

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  • DOI: https://doi.org/10.1007/s00521-012-0975-5

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