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

2026-07-20

AI Summary

Traditional “edge of chaos” criteria struggle to accurately guide the optimal design of reservoir computing for prediction tasks, thereby limiting performance gains. This work addresses this limitation by analyzing the collective dynamics of teacher-forced reservoirs and reveals that the target dynamics are primarily captured by input-modulated stable Lyapunov modes. Building on this insight, the authors propose a novel “stability–expressivity transition index” to precisely identify the optimal spectral radius. This metric overcomes the heuristic constraints of edge-of-chaos approaches and consistently locates optimal parameters across diverse chaotic and quasiperiodic target systems as well as reservoir architectures with varying symmetries, leading to significantly enhanced autonomous prediction performance.

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.

Problem

• reservoir computing
• edge of chaos
• spectral radius
• forecasting performance
• Lyapunov modes

Innovation

• reservoir computing
• edge of chaos
• Lyapunov modes
• stability-expressivity trade-off
• spectral radius