Presentation on Zoom

Note: This is an invited guest lecture as part of the course ELE6953KE Network Models, Systems and Games at Polytechnique Montreal. Jointly organized by GERAD and Polytechnique Montreal.

Graphons are powerful tools for modeling large-scale graphs, serving both as limit objects for dense graph sequences and as generative models for random graphs. This bootcamp introduces graphons from a machine learning (ML) perspective, with an emphasis on their applications in graph information processing and graph neural networks (GNNs). We will begin with the mathematical foundations of graphon theory, including homomorphism densities, cut distance, sampling, dense graph convergence, and convergence of spectra. From there, we explore how graphons can be used to formalize the convergence of convolutional architectures on convergent sequences of graphs, and what this reveals about the transferability of GNNs trained on subsampled graph data. We will also discuss recent advances in graphon-based ML, practical limitations of the graphon model in modern ML, and alternative approaches for capturing structure in sparser large graphs.

Bio: Luana Ruiz received the Ph.D. degree in electrical engineering from the University of Pennsylvania in 2022, and the M.Eng. and B.Eng. double degree in electrical engineering from the École Supérieure d'Electricité and the University of São Paulo in 2017. She is an Assistant Professor with the Department of Applied Mathematics and Statistics and the MINDS and DSAI Institutes at Johns Hopkins University, as well as the Electrical and Computer Engineering and Computer Science departments (by courtesy). Luana's work focuses on large-scale graph information processing and graph neural network architectures. She was awarded an Eiffel Excellence scholarship from the French Ministry for Europe and Foreign Affairs between 2013 and 2015; nominated an iREDEFINE fellow in 2019, a MIT EECS Rising Star in 2021, a Simons Research Fellow in 2022, and a METEOR fellow in 2023; and received best student paper awards at the 27th and 29th European Signal Processing Conferences. Luana is currently a member of the Machine Learning for Signal Processing Technical Committee of the IEEE Signal Processing Society. Web: https://luanaruiz9.github.io/