Next Wednesday July 1, 2026 our team member Antonio Álvarez-López will present his PhD Thesis on:
“Deep Learning with Controlled Flows: Expressivity, Generalization and Generation”
Advisors:
• Prof. Enrique Zuazua, FAU – Friedrich Alexander-Universität Erlangen-Nürnberg (Germany)
• Prof. Rafael Orive, Autonomous University of Madrid (UAM)
Abstract. This thesis studies deep learning from the perspective of controlled dynamical systems, with particular emphasis on neural ODEs. The central idea is to view learning as the selection of time-dependent controls in a dynamical system so that the induced flow satisfies a data-driven objective. The first part of the thesis studies supervised learning from a constructive perspective, setting the parameters as piecewise constants. We first formulate classification as a relaxed simultaneous controllability problem and develop constructive methods seeking for minimax complexity bounds. For regression, we study exact interpolation for several neural ODE architectures and establish explicit trade-offs between width and depth, where depth is measured by the number of control switches. Finally, we address generalization via the proposed notion of simultaneous cell controllability, which leads to explicit population risk bounds.
The second part is devoted to generative modeling. In this setting, learning is formulated as the transport of a base distribution toward a target distribution through controlled flows. We investigate universality with respect to Wasserstein and total variation distances, relating to the point interpolation capacity of the system. We also obtain constructive approximation results for continuous normalizing flows under suitable tail assumptions.
The third part illustrates the scope of this dynamical framework in two directions: modeling distributional dynamics from snapshot data, motivated by digital health applications, and the mean-field analysis of Transformer-type attention dynamics on the sphere, where we characterize the discrete structure of stationary measures.
WHEN
Wed. July 1, 2026 at 16:30H (Madrid time)
WHERE
On-site / Online
On-site: Sala de Grados, Module 08. Faculty of Sciences. Universidad Autónoma de Madrid. Madrid, Spain
Online: (Teams): https://teams.microsoft.com/meet/370251944267864?p=G5ZbExmZwVAxvkxSDk
Board of examiners
• Prof. Dr. Davide Barbieri
• Prof. Dr. José Antonio Carrillo
• Prof. Dr. Massimo Fornasier
• Prof. Dr. Julia Novo
• Prof. Dr. Emmanuel Trélat
|| You might like: Upcoming events
