突破混沌边缘理论，提出稳定性与表达力平衡的新指标
Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting
- 以谱半径为控制参数，发现最佳预测性能不在混沌边缘
- 稳定李雅普诺夫模态受输入调制，主导目标动态表示
- 新指标可精准定位最优谱半径，适用于多种系统结构
混沌边缘启发式长期指导着蓄水池计算机的设计，但其对模型性能的影响仍不明确。本文以蓄水池网络的谱半径为控制参数，发现最佳预测性能对应的谱半径并不等于孤立、教师强制或闭环生成蓄水池的李雅普诺夫混沌边缘。通过对教师强制蓄水池集体动力学分析，发现目标动态主要由稳定李雅普诺夫模态表示，且这些模态的有限时间稳定性强烈受输入调制。这一发现催生了稳定性-表达力转移指数，该指数在混沌与准周期目标下，对非对称和对称蓄水池结构均能准确识别自主预测的最优谱半径。
原文摘要 · Abstract (English)
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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