Learn to Synchronize, Synchronize to Learn
This work provides theoretical insights into a widely used but partially understood machine learning paradigm, which is incremental as it builds on existing RC research.
The paper tackles the problem of understanding the guiding principles behind Reservoir Computing by analyzing the role of Generalized Synchronization in training, showing that it enables the reservoir to correctly encode the input signal's generating system and that ergodicity allows the learning to generalize across multiple trajectories.
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.