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Dimension of reservoir computers.

T L Carroll1

  • 1US Naval Research Lab, Washington, DC 20375, USA.

Chaos (Woodbury, N.Y.)
|February 5, 2020
PubMed
Summary

This study reveals reservoir computing systems operate on low-dimensional surfaces. Modifying the spectral radius impacts fractal dimension and increases testing errors in these complex dynamical systems.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Computational neuroscience

Background:

  • Reservoir computing utilizes complex dynamical systems with nonlinear nodes driven by a common signal.
  • Understanding the dimensionality of these systems is crucial for analyzing their behavior and performance.

Purpose of the Study:

  • To estimate the dimension of reservoir dynamical systems.
  • To investigate the relationship between spectral radius, fractal dimension, and testing error.

Main Methods:

  • Employed three dimension estimation methods: false nearest neighbor, covariance dimension, and Kaplan-Yorke dimension.
  • Analyzed signals within the reservoir system.
  • Varied the spectral radius of the reservoir network.

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Main Results:

  • Signals within the reservoir system were found to reside on a relatively low-dimensional surface.
  • Increasing the spectral radius of the reservoir network led to an increase in the fractal dimension of the reservoir signals.
  • This increase in fractal dimension correlated with a rise in testing error.

Conclusions:

  • Reservoir computing systems exhibit low-dimensional dynamics.
  • The spectral radius is a key parameter influencing the fractal dimension and predictive accuracy of reservoir computers.
  • Controlling spectral radius is important for optimizing reservoir computing performance.