发表机构
Cornell University; Cinvestav; Universidad Nacional Autónoma de México（康奈尔大学; 墨西哥国立自治大学高级研究中心; 墨西哥国立自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从KKL观测器视角揭示储层计算的理论基础，证明其预测能力源于观测器内模原理，并推导预测误差上界，为RC架构选择提供理论指导。
AI 中文摘要
储层计算（RC）是一种用于数据驱动动力学建模的机器学习技术，广泛应用于预测和控制领域，主要在计算机科学和物理学文献中研究，在神经网络学习、物理计算和神经科学中具有广阔的应用前景。为什么储层能够学习以及如何选择良好的储层架构被认为是重要的开放性问题。我们证明，RC问题在数学上是系统与控制理论中经典问题——Kazantzis-Kravaris-Luenberger（KKL）观测器设计问题的扩展。因此，许多被认为对RC开放的问题可以从成熟的KKL文献中的大量理论中受益，这些问题非穷举地包括嵌入、横向稳定性、局部和全局唯一性保证以及有效的数据驱动解构造。基于这一联系，我们表明储层令人惊讶的预测能力实际上是众所周知的观测器内模原理的直接结果，推导了固定预测范围内预测误差的上界，并部分解释了为什么RC中的线性读出训练效果相当好。这项工作展示了系统与控制中的经典思想如何为现代机器学习方法提供强有力的理论支持并开辟新的问题。
英文摘要
Reservoir computing (RC) is a machine learning technique for data-driven modeling of dynamics for forecasting and control, primarily studied in computer science and physics literature with promising applications in neural network learning, physical computing, and neuroscience. Why reservoirs learn and how to choose good reservoir architectures are considered important open questions. We show that the RC problem is mathematically an extension of a classic problem in systems and control theory, the Kazantzis-Kravaris-Luenberger (KKL) observer design problem. As a consequence, many of the questions considered open for RC stand to benefit from a large body of theory in the mature KKL literature, non-exhaustively including on questions of embedding, transverse stability, local and global uniqueness guarantees, and effective data-driven solution constructions. Elaborating on this connection, we show that the surprising forecasting ability of reservoirs is in fact a direct consequence of the well-known observer internal model principle, derive an upper bound on the prediction error over a fixed forecast horizon, and provide a partial explanation for why linear readout training in RC works reasonably well. This work illustrates how classical ideas from systems and control can provide strong theoretical backing and open new questions for modern machine learning methods.
Comments8 pages
