Constraints on parameter choices for successful reservoir computing

TL;DR

This paper investigates the parameter conditions necessary for successful reservoir computing, specifically echo-state networks, to synchronize with and predict input time series, highlighting the importance of certain key parameters and information availability.

Contribution

It identifies critical parameters and conditions, including phase space information, that determine when echo-state networks can effectively predict time series.

Findings

Synchronization is necessary but not sufficient for prediction.

Prediction success depends on key parameter regions and information availability.

Full phase space information enhances prediction performance.

Abstract

Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the network may synchronize with the driving signal. Exploiting this synchronization, the echo-state network may be trained to autonomously reproduce the input dynamics, enabling time-series prediction. However, while synchronization is a necessary condition for prediction, it is not sufficient. Here, we study what other conditions are necessary for successful time-series prediction. We identify two key parameters for prediction performance, and conduct a parameter sweep to find regions where prediction is successful. These regions differ significantly depending on whether full or partial phase space information about the input is provided to the network during training. We explain how these regions emerge.