Control and Machine Learning
报告专家：Enrique Zuazua教授（德国埃尔朗根-纽伦堡大学）
报告时间：2024年1月18日上午9:00-10:00
报告地点：西南中心516
报告摘要：In these lectures we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning, Universal Approximation and Normalizing flows.
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 ResNet, 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 in terms of the structure of the data set.
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, exploring the interplay between depth and width of the neural network. This lecture is inspired in joint work, among others, with Domènec Ruiz-Balet (Imperial College), Borjan Geshkovski (MIT), Martin Hernandez (FAU) and Antonio Lopez and Rafael Orive (UAM-Madrid).
邀请人：张旭
