Spectral Filtering for Complex Linear Dynamical Systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909026410823680 |
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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 |