将下一代储备池计算拓展至无限维特征，提升时序预测性能。
Infinite-dimensional next-generation reservoir computing
- 将NG-RC建模为核岭回归，实现高效训练。
- 支持无穷多滞后变量和多项式特征，突破传统限制。
- 理论完备且在多个任务中优于经典方法，适合时序建模研究者。
下一代储备池计算（NG-RC）因其在复杂系统时空预测中的优异表现和易于实现而受到广泛关注。本文表明，NG-RC可被编码为核岭回归，使训练在高维多项式特征空间下依然高效可行。此外，该方法可扩展至无穷多个协变量，使模型对过去滞后的依赖以及多项式协变量数量等关键超参数不再敏感，从而摆脱传统NG-RC的限制。我们证明该方法具有坚实的理论基础，其行为符合已有文献中关于核泛化性的性质。多种数值实验显示，这些推广后的NG-RC在多个预测任务中均优于传统方法。
原文摘要 · Abstract (English)
Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a kernel ridge regression that makes training efficient and feasible even when the space of chosen polynomial features is very large. Additionally, an extension to an infinite number of covariates is possible, which makes the methodology agnostic with respect to the lags into the past that are considered as explanatory factors, as well as with respect to the number of polynomial covariates, an important hyperparameter in traditional NG-RC. We show that this approach has solid theoretical backing and good behavior based on kernel universality properties previously established in the literature. Various numerical illustrations show that these generalizations of NG-RC outperform the traditional approach in several forecasting applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。