Machine Learning and Control: Foundations, Advances, and Perspectives

Zuazua E (2026)

Publication Language: English

Publication Status: Published

Publication Type: Conference contribution, Abstract of lecture

Future Publication Type: Conference contribution

Publication year: 2026

Publisher: Proceedings of the International Congress of Mathematicians 2026. SIAM

Series: Proceedings of the International Congress of Mathematicians 2026

Book Volume: 7

Pages Range: 267-286

Conference Proceedings Title: International Congress of Mathematicians 2026

Event location: Philadelphia US

DOI: https://epubs.siam.org/doi/book/10.1137/1.ICM26

Open Access Link: https://arxiv.org/abs/2510.03303

Abstract

Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new insights into the classification and representation properties of deep neural networks while the control and optimization of static systems can be employed to better understand the performance of shallow networks. Inspired by the classical concept of turnpike, we also explore the relationship between dynamic and static neural networks, where depth is traded for width, and the role of transformers as mechanisms for accelerating classical neural network tasks. We also exploit the expressive power of neural networks (exemplified, for instance, by the Universal Approximation Theorem) to develop a novel hybrid modeling methodology, the Hybrid-Cooperative Learning (HYCO), combining mechanics and data-driven methods in a game-theoretic setting. Finally, we describe how classical properties of diffusion processes, long established in the context of partial differential equations, contribute to explaining the success of modern generative artificial intelligence (AI). We present an overview of our recent results in these areas, illustrating how control, machine learning, numerical analysis, and partial differential equations come together to motivate a fertile ground for future research.

How to cite

APA:

Zuazua, E. (2026, July). Machine Learning and Control: Foundations, Advances, and Perspectives. Paper presentation at ICM2026. International Congress of Mathematicians 2026, Philadelphia, US.

MLA:

Zuazua, Enrique. "Machine Learning and Control: Foundations, Advances, and Perspectives." Presented at ICM2026. International Congress of Mathematicians 2026, Philadelphia Ed. Susan Friedlander, Yuri Tschinkel, Proceedings of the International Congress of Mathematicians 2026. SIAM, 2026.

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