Theses
THESIS PRE-DEFENSE -- Deep Learning with Controlled Flows: Expressivity, Generalization and Generation
Speaker: Antonio Álvarez López ()Advisor/s: Enrique Zuazua Iriondo (UAM), Rafael Orive Illera (UAM-ICMAT)Date: Thursday, 14 May 2026 - 17:00Place: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
This thesis develops a mathematical framework for deep learning models based on controlled flows, with particular emphasis on neural ODEs. Its 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. Under this viewpoint, expressivity becomes a controllability problem, while statistical performance is tied to the regularity and complexity of the underlying dynamics. The thesis provides a unified controllability-based perspective on expressivity, approximation, generalization, and generative modeling in continuous-depth learning systems.
