发表机构
CentraleSupélec; Université de Lorraine; LMOPS EA-4423 Laboratory（中央超导学院; 洛林大学; LMOPS EA-4423实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究水库计算中任务相关信息在状态空间的组织，引入特征谱分解框架量化逐度表示能量，发现大量信息处理能力或存于低能量模式，表明有用的水库计算取决于维度扩展和信息几何组织。
AI 中文摘要
水库计算利用非线性动力系统将时间输入编码到高维状态空间表示中。虽然水库性能常通过记忆、非线性及其权衡来表征，但这些总体度量并未揭示任务相关信息在状态空间中是如何组织的。本文引入一个特征谱分解框架，将逐度信息处理能力与相应状态空间模式联系起来。由此能够量化逐度表示能量，并表明在某些情况下，大量信息处理能力可能存在于易受实验噪声影响的低能量模式中。这些结果表明，有用的水库计算不仅取决于维度扩展，还取决于任务相关信息的几何组织，这对物理水库计算机有直接影响。
英文摘要
Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.
