Consistency capacity of reservoir computers

TL;DR

This paper introduces a method to analyze the information processing capacity of reservoir computers, revealing how signals propagate and interfere within these systems using correlation analysis and capacity measures.

Contribution

It presents a novel framework for assessing the consistency and capacity of reservoir computers, including multiple input interference and nonlinear fading memory profiles.

Findings

Consistency spectra and capacities characterize nonlinear dependence on inputs.

Hierarchy of capacity measures reveals signal interference effects.

Time-resolved capacity profiles show nonlinear fading memory.

Abstract

We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as a reservoir computers. A multivariate correlation analysis in tailored replica tests reveals consistency spectra and capacities of a reservoir. These measures provide a high-dimensional portrait of the nonlinear functional dependence on the inputs. For multiple inputs a hierarchy of capacity measures characterizes the interference of signals from each source. For each input the time-resolved capacity forms a nonlinear fading memory profile. We illustrate the methodology with various types of echo state networks.