Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting
2026-07-20 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied a common idea called the edge-of-chaos, which is often used to design reservoir computers for better predictions. They found that the best setting for the reservoir does not match the traditional edge-of-chaos point defined by the system’s stability. Instead, by looking at how the system’s dynamics balance being stable and expressive, they created a new measure that better predicts the optimal setup for making forecasts. This holds true across different types of target data and reservoir structures.
reservoir computingedge-of-chaosspectral radiusLyapunov exponentteacher-forced reservoirautonomous forecastingchaotic dynamicsquasiperiodic dynamicsstability-expressivity indexcollective dynamics
Authors
Yao Du, Xingang Wang
Abstract
The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.