提出谱滤波方法，实现复杂动态系统无维度依赖的高效学习。
Spectral Filtering for Complex Linear Dynamical Systems
- 基于Slepian基的谱滤波，捕捉振荡与长记忆特性。
- 在单位圆扇区内的谱条件下，实现无维度后悔上界。
- 适合信号处理、量子系统等含振荡动态的研究者。
我们研究了具有扇形有界谱的复值线性动态系统（CLDS）的学习问题。这类系统能捕捉信号处理、结构化状态空间模型及量子系统中的振荡与长记忆动态。本文提出一种基于Slepian基的谱滤波方法，证明可学习性由一个与环境状态维度无关的有效维度决定。因此，在谱包含于单位圆扇区的CLDS中，实现了无维度的序列预测后悔上界。
原文摘要 · Abstract (English)
We study the problem of learning complex-valued linear dynamical systems (CLDS) with sector-bounded spectrum. This class captures oscillatory and long-memory dynamics arising in signal processing, structured state space models, and quantum systems. We introduce a spectral filtering method based on the Slepian basis and show that learnability is governed by an effective dimension independent of the ambient state dimension. As a consequence, we obtain dimension-free regret bounds for sequence prediction in CLDS with spectrum contained in a sector of the unit disk.
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