# Chasing the Echo State Property

arXiv: https://arxiv.org/abs/1811.10892 · HTML: https://mlsanity.com/paper/1811.10892/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2018.

## Built on by (most cited first, 5 of 5)

- [A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning](https://mlsanity.com/paper/2307.15092/) (2023)
- [Edge of stability echo state networks](https://mlsanity.com/paper/2308.02902/) (2023)
- [PyRCN: A Toolbox for Exploration and Application of Reservoir Computing Networks](https://mlsanity.com/paper/2103.04807/) (2021)
- [Optimal input representation in neural systems at the edge of chaos](https://mlsanity.com/paper/2107.05709/) (2021)
- [Rethinking Reservoir Pruning: A Dynamical Perspective for Echo State Networks](https://mlsanity.com/paper/2608.04593/) (2026)

## Abstract (arXiv)

Reservoir Computing (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to stability constraints specified by the Echo State Property (ESP). Literature conditions for the ESP typically fail to properly account for the effects of driving input signals, often limiting the potentialities of the RC approach. In this paper, we study the fundamental aspect of asymptotic stability of RC models in presence of driving input, introducing an empirical ESP index that enables to easily analyze the stability regimes of reservoirs. Results on two benchmark datasets reveal interesting insights on the dynamical properties of input-driven reservoirs, suggesting that the actual domain of ESP validity is much wider than what covered by literature conditions commonly used in RC practice.