Quantitative evaluation of the performance of discrete-time reservoir computers in the forecasting, filtering, and reconstruction of stochastic stationary signals

TL;DR

This paper extends the concept of information processing capacity in reservoir computing to non-independent signals, demonstrating its effectiveness in forecasting, filtering, and reconstructing stochastic stationary signals with improved performance over traditional methods.

Contribution

It introduces a generalized capacity measure for reservoir computing with autocorrelated inputs and validates its effectiveness in stochastic signal processing tasks.

Findings

Reservoir computing satisfies separation and fading memory properties.

RC significantly outperforms standard techniques in certain stochastic forecasting tasks.

The model effectively handles autocorrelated input signals in filtering and reconstruction.

Abstract

This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering problems for which we explicitly compute this generalized capacity as a function of the reservoir parameter values using a streamlined model. The reservoir model leading to these developments is used to show that, whenever that approximation is valid, this computational paradigm satisfies the so called separation and fading memory properties that are usually associated with good information processing performances. We show that several standard memory, forecasting, and filtering problems that appear in the parametric stochastic time series context can be readily formulated and tackled via RC which, as we show, significantly outperforms standard techniques in some instances.