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Low dimensional manifolds in reservoir computers.

T L Carroll1

  • 1U.S. Naval Research Lab, Washington, DC 20375, USA.

Chaos (Woodbury, N.Y.)
|July 12, 2021
PubMed
Summary

This study reveals how reservoir computer (RC) parameters influence performance on signal estimation tasks. Optimizing node coupling and controlling the largest Lyapunov exponent enhances RC performance, independent of network sparsity.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Machine learning

Background:

  • Reservoir computers (RCs) are dynamical systems with numerous nonlinear nodes driven by a common signal.
  • Despite high dimensionality, RC variables evolve on a lower-dimensional manifold.
  • Understanding this manifold is key to optimizing RC performance.

Purpose of the Study:

  • To investigate the relationship between reservoir computer parameters and manifold dimension.
  • To determine how manifold dimension affects signal estimation performance.
  • To identify optimal parameter configurations for enhanced reservoir computing.

Main Methods:

  • Analysis of reservoir computer dynamics and manifold dimension.
  • Varying node coupling and controlling the largest Lyapunov exponent.

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  • Evaluating performance on a signal estimation task.

    • Main Results:

    • Manifold dimension is dependent on reservoir computer parameters.
    • Increasing node coupling, while controlling the largest Lyapunov exponent, optimizes performance.
    • Network sparsity does not influence reservoir computer performance.

    Conclusions:

    • Reservoir computer performance is tunable via parameter optimization.
    • Controlling the interplay between node coupling and system stability is crucial.
    • Sparsity is not a critical factor for effective reservoir computing.