Nonlinear memory capacity of parallel time-delay reservoir computers in the processing of multidimensional signals

TL;DR

This paper develops a theoretical model for parallel delay-based reservoir computers handling multidimensional signals, analyzing their nonlinear memory capacity and validating findings through empirical experiments.

Contribution

It introduces an explicit functional link between reservoir parameters and performance, and assesses the impact of finite sample training on reservoir capacity.

Findings

Theoretical model accurately predicts empirical performance.

Parallel architectures show robustness to task misspecification.

Finite sample training reduces reservoir capacity.

Abstract

This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir parameters and architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context is used to assess the impact of finite sample training on the decrease of the reservoir capacity. Finally, an empirical study is conducted that shows the adequacy of the theoretical results with the empirical performances exhibited by various reservoir architectures in the execution of several nonlinear tasks with multidimensional inputs. Our results confirm the robustness properties of the parallel reservoir architecture with respect to task misspecification and parameter choice that had already been documented in the literature.