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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 online 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 nonlinear dynamics are learnable. These insights motivate a new neural architecture, the Spectral Transform Unit (STU), which achieves state-of-the-art performance on language modeling and dynamical system benchmarks.
Elad Hazan (Princeton University)
Professor of Computer Science
Elad Hazan is a professor of computer science at Princeton University. His research focuses on the design and analysis of algorithms for basic problems in machine learning and optimization. Among his contributions are the co-invention of the AdaGrad algorithm for deep learning, the first sublinear-time algorithms for convex optimization, and online nonstochastic control theory. He is the recipient of the Bell Labs Prize, the IBM Goldberg best paper award twice, a European Research Council grant, a Marie Curie fellowship, Google Research Award and is an ACM fellow. He served on the steering committee of the Association for Computational Learning and was program chair for the Conference on Learning Theory 2015. He is the co-founder and director of Google AI Princeton.
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