储层计算中的内模原理
The internal model principle in reservoir computing
- University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文以内模原理统一储层计算的学习机制，通过信号发生器建模训练信号，建立与输出调节、观测器及频域插值的联系，并解释预测器不稳定性以指导设计。
AI中文摘要：
本文通过内模原理的视角研究储层计算系统中的学习问题。核心思想是将训练信号建模为外生信号发生器的输出，从而将储层计算与输出调节、观测器理论和频域插值联系起来。对于线性信号发生器，我们通过不变子空间刻画线性储层的稳态响应，建立了与Luenberger观测器和经典频域插值的联系。对于非线性信号发生器，我们利用不变流形获得类似结果，将同步与Kazantzis-Kravaris/Luenberger观测器联系起来，并将读出训练与非线性矩匹配联系起来。案例研究说明了我们的视角如何解释训练预测器可能的不稳定性，并为储层设计提供指导。
英文摘要：
The paper studies learning in reservoir computing systems through the lens of the internal model principle. The key idea is to model training signals as outputs of an exogenous signal generator, thus connecting reservoir computing to output regulation, observer theory, and frequency-domain interpolation. For linear signal generators, we characterize the steady-state response of a linear reservoir through invariant subspaces, establishing connections with Luenberger observers and classical frequency-domain interpolation. For nonlinear signal generators, we obtain analogous results using invariant manifolds, connecting synchronization to Kazantzis-Kravaris/Luenberger observers and readout training to nonlinear moment matching. Case studies illustrate how our perspective explains possible instability of trained predictors and informs reservoir design.
