# Learn to Synchronize, Synchronize to Learn

arXiv: https://arxiv.org/abs/2010.02860 · HTML: https://mlsanity.com/paper/2010.02860/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Learning strange attractors with reservoir systems](https://mlsanity.com/paper/2108.05024/) (2021)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)
- [Recurrences reveal shared causal drivers of complex time series](https://mlsanity.com/paper/2301.13516/) (2023)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Learning unidirectional coupling using echo-state network](https://mlsanity.com/paper/2303.13562/) (2023)
- [Euler State Networks: Non-dissipative Reservoir Computing](https://mlsanity.com/paper/2203.09382/) (2022)
- [Harnessing omnipresent oscillator networks as computational resource](https://mlsanity.com/paper/2502.04818/) (2025)
- [Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2605.12683/) (2026)

## Abstract (arXiv)

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.