驱动临界性连接通用计算与最优表示
Driven criticality links universal computation and optimal representations
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中文总结 AI 辅助
研究近临界动力学与增强计算潜在机制不明问题，在储层计算中扩展通用性结果，引入相关指数，发现邻域可分性等在边缘驱动稳定性窄窗口优化，在共同框架内连接多方面特性。
中文摘要 AI 辅助
近临界动力学常与增强计算相关，但潜在机制不明。我们在储层计算中解决此问题，固定循环网络将输入序列映射到高维状态，仅训练简单读出。我们将固定储层通用性结果扩展到离散时间输入驱动储层，并将其关键几何条件邻域分离与动力学联系起来。为此引入有限分辨率邻域可分性指数和输入条件最大李雅普诺夫指数。发现邻域可分性、混沌时间序列预测和平滑高维表示几何在边缘驱动稳定性的同一窄窗口中得到优化。在此 regime 中，协方差谱接近近最优平滑表示预期的幂律缩放。结果在共同动力学框架内连接不稳定边缘计算、通用性、读出性能和最优表示几何。
英文摘要
Near-critical dynamics are often linked to enhanced computation, but the underlying mechanism remains unclear. We address this question in reservoir computing, where a fixed recurrent network maps input sequences into high-dimensional states and only a simple readout is trained. We extend fixed-reservoir universality results to discrete-time input-driven reservoirs and connect their key geometric condition, neighborhood separation, to dynamics. To this end, we introduce a finite-resolution neighborhood separability index and an input-conditioned maximal Lyapunov exponent. We find that neighborhood separability, chaotic time-series prediction, and smooth high-dimensional representation geometry are optimized in the same narrow window of marginal driven stability. In this regime, the covariance spectrum approaches the power-law scaling expected for near-optimal smooth representations. Our results link edge-of-instability computation, universality, readout performance, and optimal representation geometry within a common dynamical framework.
