Arrivederci, Paolo

Paolo Zuzolo, who already had been a guest at ZESS for a talk in 2024 had returned for a longer research stay to collaborate with the DFG Research Unit “Learning to Sense”. Specifically, he worked on Shape Matching and Neural Network Training.

Shape matching aims to determine how two geometric objects correspond to each other, even under strong non-rigid deformations, as in matching a hippopotamus to a giraffe. This underlies many tasks in Computer Vision and Graphics, including retrieval, animation, and morphing.
Partial shape matching addresses the even harder setting where only a subset of a shape is available—due to occlusions, missing geometry, or clutter. A core difficulty is localizing this subset on the full shape, since missing parts, deformations, and intrinsic symmetries make the correct region ambiguous without explicit correspondences.   A useful idea in this context is to tailor the mathematical tools so that they naturally relates to some regions of a shape and less to others. When this happens, the resulting “spectral fingerprints” become more focused and expressive, which can greatly help in figuring out where a partial shape belongs on a complete shape.

Training neural networks becomes especially difficult when the loss landscape is highly non-convex—meaning it’s full of hills, valleys, and flat regions that make it hard for the usual learning procedure to reliably point the model in the right direction.
We tackle that challenge with a hybrid optimization method that mixes the model’s standard learning cues with an additional correction computed at the network’s output, one that accounts for the local shape of the landscape.
By enriching the update information with this shape-aware adjustment, the approach helps the model navigate complicated regions of the loss surface more effectively. The result is a training procedure that stays efficient while aiming for faster convergence, smoother and more stable learning dynamics.

Paolo Zuzolo received the M.S. degree in Mathematics with the University of Bologna, Italy in 2020, and he is currently a Ph.D. student in Mathematics with the same University. After completing his master, with a thesis on processing and visualization of astrophysical data, he worked as researcher and developer at CINECA, Bologna, Italy, at the Visualization Information Technology Laboratory. His research interests include Numerical Methods for Geometry Processing and Geometric Deep Learning.

Thanks for being with us, Paolo, hope to see you again soon!