Learning in Dynamical Systems

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• Elad Hazan (Princeton University)
• Wednesday 29 October 2025, 13:00-14:00
• Centre for Mathematical Sciences, MR14.

If you have a question about this talk, please contact Georg Maierhofer.

Learning in dynamical systems is a fundamental challenge underlying modern sequence modeling. Despite extensive study, efficient algorithms with formal guarantees for general nonlinear systems have remained elusive. This talk presents a provably efficient framework for learning in any bounded and Lipschitz nonlinear dynamical system, establishing the first sublinear regret guarantees in a dimension-free setting. Our approach combines Koopman lifting, Luenberger observers, and, crucially, spectral filtering to show that a broad class of nonlinear dynamics are learnable. These insights motivate a new neural architecture, the Spectral Transform Unit (STU), which we will describe and present preliminary experiments on open benchmarks of language modelling and dynamical systems.

This talk is part of the Applied and Computational Analysis series.

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