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Stability of Gated Recurrent Unit Neural Networks: Convex Combination Formulation Approach

Author

Listed:
  • Dušan M. Stipanović

    (University of Illinois at Urbana-Champaign)

  • Mirna N. Kapetina

    (University of Novi Sad)

  • Milan R. Rapaić

    (University of Novi Sad)

  • Boris Murmann

    (Stanford University)

Abstract

In this paper, a particular discrete-time nonlinear and time-invariant system represented as a vector difference equation is analyzed for its stability properties. The motivation for analyzing this particular system is that it models gated recurrent unit neural networks commonly used and well known in machine learning applications. From the technical perspective, the analyses exploit the systems similarities to a convex combination of discrete-time systems, where one of the systems is trivial, and thus, the overall properties are mostly dependent on the other one. Stability results are formulated for the nonlinear system and its linearization with respect to the systems, in general, multiple equilibria. To motivate and illustrate the potential of these results in applications, some particular results are derived for the gated recurrent unit neural network models and a connection between local stability analysis and learning is provided.

Suggested Citation

  • Dušan M. Stipanović & Mirna N. Kapetina & Milan R. Rapaić & Boris Murmann, 2021. "Stability of Gated Recurrent Unit Neural Networks: Convex Combination Formulation Approach," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 291-306, January.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01776-w
    DOI: 10.1007/s10957-020-01776-w
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    References listed on IDEAS

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    1. D.M. Stipanović & D.D. Šiljak, 2002. "Connective Stability of Discontinuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 711-726, December.
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