Date: Thursday, October 9, 2025
Time: 2:00 pm
Location: Seminar room EXP-610

Speaker: Marco Pacini (University of Trento & Fondazione Bruno Kessler, visiting Northeastern University)
Title:  On Universality of Equivariant Neural Networks

Abstract:  Equivariant neural networks provide a principled way to incorporate symmetry into learning architectures and are studied for both their empirical success and mathematical structure. In this talk, we first discuss their separation power—the ability to distinguish inputs up to symmetry—which is a well-understood and necessary condition for approximation. We then examine their approximation capabilities, which remain less well understood. Focusing on equivariant shallow networks, we show that architectures with the same separation power may nevertheless approximate different classes of functions, demonstrating that separation is a necessary but not sufficient condition for universality.
The talk is based on joint works with Xiaowen Dong, Bruno Lepri, Gabriele Santin, Shubhendu Trivedi, Mircea Petrache and Robin Walters.

Biography:    Marco Pacini’s research focuses on the fundamental principles of Geometric Deep Learning and Equivariant Machine Learning. Some of his research interests include the constructive characterization of equivariant models, as well as their expressivity and approximation capabilities.