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Generalization and Efficient Training of Graph Neural Networks

Juan Cervino, Postdoctoral Researcher in the Laboratory for Information and Decision Systems (LIDS) at the Massachusetts Institute of Technology

601 Computer Studies Building

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still lacking. In this talk, we take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain. As demonstrated empirically, we prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale and increase linearly with the spectral continuity constants of the filter functions. Notably, our theory explains both node-level and graph-level tasks. In the second part of the talk, we will deal with efficient GNN training, motivated by the fact that on large-scale graphs convolutions incur high computational costs, leading to scalability limitations. We propose a novel algorithm to learn GNNs on large-scale graphs that, starting from a moderate number of nodes, successively increases the size of the graph during training. This algorithm is further benchmarked on a decentralized control problem, where it retains comparable performance to its large-scale counterpart at a reduced computational cost. The talk will finish discussing future and ongoing projects.

 Bio: Juan is a postdoctoral researcher in the Laboratory for Information and Decision Systems (LIDS) at the Massachusetts Institute of Technology, hosted by Professor Navid Azizan. Previously, he was a PhD student in the Department of Electrical and Systems Engineering (ESE) at the University of Pennsylvania, supervised by Professor Alejandro Ribeiro. In 2023, Juan was named a Rising Star in Signal Processing. He received his B.Sc. degree in Electrical Engineering from the Universidad de la República Oriental del Uruguay, Montevideo, in 2018. His current research interests include (graph) machine learning, signal processing, optimization, and control. https://juancervino.github.io/.