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Spectral Filtering for General Linear Dynamical Systems

arXiv 1802.03981 ↗First posted 12 Feb 2018cs.LG cs.SY eess.SYcited by 37

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Abstract (arXiv)

We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a symmetric transition matrix, using a novel convex relaxation to allow for the efficient identification of phases.

Key facts. Cited by 37 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Feb 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 7; 2024: 8; 2025: 7; 2026: 5.

37 papers.

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  1. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  2. 2023Spectral State Space Modelscited by 21
  3. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  4. 2023Unconstrained Dynamic Regret via Sparse Codingcited by 11
  5. 2023Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscited by 10
  6. 2022Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Netscited by 7
  7. 2024Flash STU: Fast Spectral Transform Unitscited by 7
  8. 2024FutureFill: Fast Generation from Convolutional Sequence Modelscited by 7
  9. 2021Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through timecited by 6
  10. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  11. 2025Universal Sequence Preconditioningcited by 6
  12. 2025Universal Learning of Nonlinear Dynamicscited by 5
25 more
  1. 2021Global Convergence Using Policy Gradient Methods for Model-free Markovian Jump Linear Quadratic Controlcited by 4
  2. 2021Time varying regression with hidden linear dynamicscited by 4
  3. 2022Fairness in Forecasting of Observations of Linear Dynamical Systemscited by 4
  4. 2023PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNscited by 4
  5. 2024Online Control in Population Dynamicscited by 3
  6. 2024Combining Federated Learning and Control: A Surveycited by 3
  7. 2024Provable Length Generalization in Sequence Prediction via Spectral Filteringcited by 3
  8. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
  9. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  10. 2026Elastic Spectral State Space Models for Train-Once Budgeted Inferencecited by 2
  11. 2022PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelscited by 1
  12. 2024The Complexity of Sequential Prediction in Dynamical Systemscited by 1
  13. 2025SpectraLDS: Provable Distillation for Linear Dynamical Systemscited by 1
  14. 2026The Power of Second Order Methods for Sequence Preconditioningcited by 1
  15. 2022System Identification via Nuclear Norm Regularizationcited by 0
  16. 2022Dynamic Structure Estimation from Bandit Feedback using Nonvanishing Exponential Sumscited by 0
  17. 2022Linear RNNs Provably Learn Linear Dynamic Systemscited by 0
  18. 2023Spectral learning of Bernoulli linear dynamical systems modelscited by 0
  19. 2024Approximated Orthogonal Projection Unit: Stabilizing Regression Network Training Using Natural Gradientcited by 0
  20. 2025Temporal Robustness in Discrete Time Linear Dynamical Systemscited by 0
  21. 2025Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacycited by 0
  22. 2025Efficient Spectral Control of Partially Observed Linear Dynamical Systemscited by 0
  23. 2026FW-NKF: Frequency-Weighted Neural Kalman Filterscited by 0
  24. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0
  25. 2026Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Modelscited by 0