Dimension of Reservoir Computers

TL;DR

This paper investigates the dimensionality of reservoir computers using three estimation methods, revealing that reservoir signals are low-dimensional and that spectral radius influences their complexity and performance.

Contribution

It introduces the application of false nearest neighbor, covariance, and Kaplan-Yorke dimensions to reservoir systems, highlighting how spectral radius affects their fractal dimension and error rates.

Findings

Reservoir signals are confined to a low-dimensional surface.

Increasing spectral radius raises the fractal dimension.

Higher fractal dimension correlates with increased testing error.

Abstract

A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the reservoir dynamical system. It is shown that the signals in the reservoir system exist on a relatively low dimensional surface. Changing the spectral radius of the reservoir network can increase the fractal dimension of the reservoir signals, leading to an increase in testing error.