Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem? We give a provable pipeline for doing so. Starting from observations of an unknown nonlinear dynamical system, we first learn an implicit spectral predictor using Observation Spectral Filtering (OSF), a convex method that competes with the best linear observer for the system. We then apply spectral-to-LDS distillation to convert this predictor into an explicit recurrent linear dynamical system. Our main theorem shows that the average prediction error of the distilled LDS decomposes into an exponentially-small distillation term...
| Authors | Liane Galanti, Devan Shah, Shlomo Fortgang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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