Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting

Yao Du, Xingang Wang
7/20/2026
nlin.CDcs.LGnlin.AO

No official code found. Best implementation: Xingang-Wang/SETI (0 stars, last commit 2026-07-20).

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.

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Code Implementations(1)

Xingang-Wang/SETICommunity70%

Reference code and data for "Beyond the edge of chaos: Stability–expressivity transfer in reservoir forecasting" (Du & Wang, PRL). Asymmetric-reservoir MATLAB pipeline + Python figure scripts + lightweight figure data.

00Jul 20, 20263 months agoNOASSERTION

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Cite this paper

@article{du2026beyond,
  title  = {Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting},
  author = {Yao Du and Xingang Wang},
  year   = {2026},
  eprint = {2607.17909},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2607.17909v1}
}

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