Dimension of Reservoir Computers
This work provides insights into the internal dynamics of reservoir computers, which could help optimize their design for machine learning tasks, though it appears incremental as it applies existing dimension estimation methods without introducing new paradigms.
The study investigated the dimensionality of reservoir computers, revealing that reservoir signals exist on a low-dimensional surface, and increasing the spectral radius raises the fractal dimension, which correlates with higher testing errors.
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.