Abstract: Variational principles have long played a fundamental role in the development of modern mathematics, physics, and scientific computing. In recent years, machine learning has introduced a transformative computational paradigm cantered on highly expressive, nonlinear function spaces and large-scale minimisation problems.
In this talk, we adopt a variational and numerical-analysis perspective on machine learning algorithms, focusing on their formulation as nonlinear minimisation problems. We examine how foundational concepts—such as stability, consistency, approximability, and compactness—acquire new interpretations within this framework, and demonstrate how the underlying continuous variational structure governs the behaviour and performance of neural-network approximations.

For further information please contact elisur.magrini@unibocconi.it