  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.
