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Deep time-delay reservoir computing: Dynamics and memory capacity.

Mirko Goldmann1, Felix Köster1, Kathy Lüdge1

  • 1Institute of Theoretical Physics, Technische Universität Berlin, Berlin D-10623, Germany.

Chaos (Woodbury, N.Y.)
|October 2, 2020
PubMed
Summary
This summary is machine-generated.

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Deep time-delay reservoir computing uses systems with time-delays for supervised learning. Its dynamical properties, like bifurcations and Lyapunov exponents, optimize memory capacity (MC) and enable enhanced configurations for linear or nonlinear tasks.

Area of Science:

  • Computational neuroscience
  • Machine learning
  • Nonlinear dynamics

Background:

  • Reservoir computing (RC) is a machine learning paradigm utilizing recurrent neural networks with fixed weights.
  • Time-delay reservoir computing (TDRC) incorporates time delays into the recurrent connections, enhancing computational capabilities.
  • Deep TDRC architectures offer increased complexity and potential for sophisticated information processing.

Purpose of the Study:

  • To investigate the relationship between the dynamical properties of a deep Ikeda-based reservoir and its memory capacity (MC).
  • To explore how these dynamical properties can be leveraged for optimizing TDRC performance.
  • To identify configurations that maximize specific degrees of MC for targeted applications.

Main Methods:

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  • Analysis of bifurcations in the autonomous system underlying the deep Ikeda reservoir.
  • Computation of conditional Lyapunov exponents to quantify generalized synchronization between input and layer dynamics.
  • Numerical simulations to observe the impact of resonances between clock cycles and layer delays on MC.

    • Main Results:

    • Memory capacity (MC) is directly related to the system's proximity to bifurcations and the magnitude of conditional Lyapunov exponents.
    • The interplay of different dynamical regimes allows for adjustable distributions between linear and nonlinear MC.
    • Resonances between clock cycle and delays can enhance, rather than degrade, MC in deep TDRC, unlike in single-layer systems.

    Conclusions:

    • The dynamical properties of deep TDRC systems provide a mechanism for optimizing memory capacity.
    • Specific configurations can be designed to achieve either high nonlinear MC or extended linear MC.
    • Understanding these dynamics enables the creation of specialized TDRC systems for diverse computational tasks.