II Workshop on Control Theory and Partial Differential Equations
On Thursday October 26, 2022 our Head Prof. Enrique Zuazua will talk on “Control and Machine Learning” as plenary speaker at the II Workshop on Control Theory and Partial Differential Equations from October 25th. to 28th, 2022 at Universidade Federal Fluminense, Brazil.
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)
Wed. October 26, 2022 at 15:00H (Berlin time)
Auditorium. Institute of Mathematics and Statistics, Universidade Federal Fluminense (Brazil)
Videos will be available at: Youtube
This workshop will be a scientific meeting with the objective of creating a discussion forum between students, teachers and researchers from teaching and research institutions, having as areas of interest 2: Partial Differential Equations and Control Theory for systems governed by PDEs. In addition to the presentation of recent works by researchers, the event also features plenary lectures and mini-courses with internationally renowned researchers.
Check the program and all details at the official page of the event
Poster of the event: