# Do Reservoir Computers Work Best at the Edge of Chaos?

arXiv: https://arxiv.org/abs/2012.01409 · HTML: https://mlsanity.com/paper/2012.01409/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 17 of 17)

- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [Seeing double with a multifunctional reservoir computer](https://mlsanity.com/paper/2305.05799/) (2023)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Dynamical stability and chaos in artificial neural network trajectories along training](https://mlsanity.com/paper/2404.05782/) (2024)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [Time Shifts to Reduce the Size of Reservoir Computers](https://mlsanity.com/paper/2205.02267/) (2022)
- [An introduction to reservoir computing](https://mlsanity.com/paper/2412.13212/) (2024)
- [Reservoir Computing with a Single Oscillating Gas Bubble: Emphasizing the Chaotic Regime](https://mlsanity.com/paper/2504.07221/) (2025)
- [Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing](https://mlsanity.com/paper/2603.14944/) (2026)
- [Neuromorphic on-chip reservoir computing with spiking neural network architectures](https://mlsanity.com/paper/2407.20547/) (2024)
- [Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos](https://mlsanity.com/paper/2606.22765/) (2026)
- [Reservoir Computing with Magnetic Thin Films](https://mlsanity.com/paper/2101.12700/) (2021)
- [Boosting Reservoir Computing with Brain-inspired Adaptive Dynamics](https://mlsanity.com/paper/2504.12480/) (2025)
- [Neuronal correlations shape the scaling behavior of memory capacity and nonlinear computational capability of reservoir recurrent neural networks](https://mlsanity.com/paper/2504.19657/) (2025)
- [Fractal and Chaotic Activation Functions in Echo State Networks: Preprocessing Topology Governs the Echo State Property](https://mlsanity.com/paper/2512.14675/) (2025)
- [Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting](https://mlsanity.com/paper/2607.17909/) (2026)

## Abstract (arXiv)

It has been demonstrated that cellular automata had the highest computational capacity at the edge of chaos, the parameter at which their behavior transitioned from ordered to chaotic. This same concept has been applied to reservoir computers; a number of researchers have stated that the highest computational capacity for a reservoir computer is at the edge of chaos, although others have suggested that this rule is not universally true. Because many reservoir computers do not show chaotic behavior but merely become unstable, it is felt that a more accurate term for this instability transition is the "edge of stability"Here I find two examples where the computational capacity of a reservoir computer decreases as the edge of stability is approached; in one case, because generalized synchronization breaks down, and in the other case because the reservoir computer is a poor match to the problem being solved. The edge of stability as an optimal operating point for a reservoir computer is not in general true, although it may be true in some cases.