# Asymptotic Stability in Reservoir Computing

arXiv: https://arxiv.org/abs/2206.03854 · HTML: https://mlsanity.com/paper/2206.03854/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Deep Randomized Neural Networks](https://mlsanity.com/paper/2002.12287/) (2020)
- [Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography](https://mlsanity.com/paper/1802.02844/) (2018)
- [Reservoir Computing meets Recurrent Kernels and Structured Transforms](https://mlsanity.com/paper/2006.07310/) (2020)
- [Photonic Delay Systems as Machine Learning Implementations](https://mlsanity.com/paper/1501.02592/) (2015)
- [Scaling up Echo-State Networks with multiple light scattering](https://mlsanity.com/paper/1609.05204/) (2016)

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

- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Comparison of Reservoir Computing topologies using the Recurrent Kernel approach](https://mlsanity.com/paper/2401.14557/) (2024)
- [Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects](https://mlsanity.com/paper/2508.03222/) (2025)
- [Thermodynamic limit in learning period three](https://mlsanity.com/paper/2405.08825/) (2024)
- [LoRA-RC: Reservoir Computing with Low-Rank Adaptation](https://mlsanity.com/paper/2609.12327/) (2026)

## Abstract (arXiv)

Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly impacts performance. In practice, it is desirable to stay in a stable regime, where the effect of perturbations does not explode exponentially, but also close to the chaotic frontier where reservoir dynamics are rich. Open questions remain today regarding input regularization and discontinuous activation functions. In this work, we use the recurrent kernel limit to draw new insights on stability in reservoir computing. This limit corresponds to large reservoir sizes, and it already becomes relevant for reservoirs with a few hundred neurons. We obtain a quantitative characterization of the frontier between stability and chaos, which can greatly benefit hyperparameter tuning. In a broader sense, our results contribute to understanding the complex dynamics of Recurrent Neural Networks.