Spectral Filtering for Complex Linear Dynamical Systems

Fuente: arXiv
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Main Authors: Hazan, Elad, Marsden, Annie
Format: Preprint
Published: 2026
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author Hazan, Elad
Marsden, Annie
author_facet Hazan, Elad
Marsden, Annie
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_22400
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Spectral Filtering for Complex Linear Dynamical Systems
Hazan, Elad
Marsden, Annie
Quantum Physics
Artificial Intelligence
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.
title Spectral Filtering for Complex Linear Dynamical Systems
topic Quantum Physics
Artificial Intelligence
url https://arxiv.org/abs/2601.22400