mlsanityData to 14 Oct 2026

Spectral Filtering for Complex Linear Dynamical Systems

arXiv 2601.22400 ↗First posted 29 Jan 2026quant-ph cs.AIcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 17 of its 21 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

17 of 21 references.

References · 17

  1. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  2. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  3. 2022Hungry Hungry Hippos: Towards Language Modeling with State Space Modelscited by 499
  4. 2022Diagonal State Spaces are as Effective as Structured State Spacescited by 350
  5. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  6. 2013Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributionscited by 60
  7. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  8. 2017Learning Linear Dynamical Systems via Spectral Filteringcited by 46
  9. 2023Universality of Linear Recurrences Followed by Non-linear Projections: Finite-Width Guarantees and Benefits of Complex Eigenvaluescited by 36
  10. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  11. 2022Introduction to Online Controlcited by 19
  12. 2020No-Regret Prediction in Marginally Stable Systemscited by 18
5 more
  1. 2020Improved rates for prediction and identification of partially observed linear dynamical systemscited by 12
  2. 2024Provable Benefits of Complex Parameterizations for Structured State Space Modelscited by 9
  3. 2024FutureFill: Fast Generation from Convolutional Sequence Modelscited by 7
  4. 2025Universal Sequence Preconditioningcited by 6
  5. 2025An Uncertainty Principle for Linear Recurrent Neural Networkscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026The Power of Second Order Methods for Sequence Preconditioningcited by 1
  2. 2026A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systemscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
  2. 2023Spectral State Space Models
  3. 2026Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems
  4. 2026Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems
  5. 2025Observability conditions for neural state-space models with eigenvalues and their roots of unity
  6. 2025Spectral Representation-based Reinforcement Learning
  7. 2026The Expressive Limits of Diagonal SSMs for State-Tracking
  8. 2026Optimal Decay Spectra for Linear Recurrences