Learn to Synchronize, Synchronize to Learn

TL;DR

This paper investigates how Generalized Synchronization (GS) influences Reservoir Computing's ability to encode input signals, providing theoretical insights and practical measurement tools for improved learning outcomes.

Contribution

It offers a theoretical analysis of GS in Reservoir Computing, identifying conditions for successful learning and introducing a practical measure via the Mutual False Nearest Neighbors index.

Findings

GS enables reservoir to encode input system dynamics effectively

Ergodicity ensures generalization across multiple input trajectories

Mutual False Nearest Neighbors index measures GS satisfaction

Abstract

In recent years, the machine learning community has seen a continuous growing interest in research aimed at investigating dynamical aspects of both training procedures and machine learning models. Of particular interest among recurrent neural networks we have the Reservoir Computing (RC) paradigm characterized by conceptual simplicity and a fast training scheme. Yet, the guiding principles under which RC operates are only partially understood. In this work, we analyze the role played by Generalized Synchronization (GS) when training a RC to solve a generic task. In particular, we show how GS allows the reservoir to correctly encode the system generating the input signal into its dynamics. We also discuss necessary and sufficient conditions for the learning to be feasible in this approach. Moreover, we explore the role that ergodicity plays in this process, showing how its presence allows the learning outcome to apply to multiple input trajectories. Finally, we show that satisfaction of the GS can be measured by means of the Mutual False Nearest Neighbors index, which makes effective to practitioners theoretical derivations.