“Ensamble Optimal Control: ResNets, Diffeomorphisms Approximation and Normalizing Flows”
Martedì 14 Novembre 2023, ore 17:00 - Aula 2AB40 - Alessandro Scagliotti (Technische Universität München - TUM | Munich Center for Machine Learning - MCML)
Abstract
In the last years it was observed that Residual Neural Networks (ResNets) can be interpreted as discretizations of control systems, bridging ResNets (and, more generally, Deep Learning) with Control Theory.
In the first part of this seminar we formulate the task of a data-driven reconstruction of a diffeomorphism as an ensemble optimal control problem.
In the second part we adapt this machinery to address the problem of Normalizing Flows: after observing some samplings of an unknown probability measure, we want to (approximately) construct a transport map that brings a “simple” distribution (e.g., a Gaussian) onto the unknown target distribution. In both the problems we use tools from $\Gamma$-convergence to study the limiting case when the size of the data-set tends to infinity.
