Optimization and Control in Burgundy

Next May 11, 2023 at 10:10H our Head Prof. Enrique Zuazua will talk on “Control and Machine Learning” at the conference Optimization and Control in Burgundy that aims to gather mathematicians from the two fields Optimization and Control to promote new exchanges and collaborations organized from May 9th-11st, 2023 at University of Burgundy, Dijon (France).

Abstract. In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning and Universal Approximation.We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control.

We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics.

This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domenec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai)

On-site / online

[On-site] Salle René Baire. 4th floor.
Dijon (campus de l’U. Bourgogne)

[Online] FAU Zoom link

Check the program at the official page of the event