Description:

Graph Neural Network Meets Random Geometric Graph

Suqi Liu, Assistant Professor, Department of Statistics, University of California, Riverside

Abstract: Graph neural networks (GNNs) have emerged as a powerful framework for learning from graph-structured data, yet their theoretical understanding—particularly regarding the behavior of different architectural choices across various graph-based tasks—remains limited. In parallel, random geometric graphs (RGGs) provide a well-defined probabilistic model that captures the interplay between geometry and connectivity in complex networks. In this talk, I will discuss several efforts I have undertaken to bridge these two perspectives by studying GNNs through the lens of RGGs. In the first part, I will focus on the classic graph matching problem and show that, by leveraging a specific GNN, perfect recovery can be achieved even in high-noise regimes. In the second part, I will briefly highlight recent work demonstrating the provable benefits of graph attention networks (GATs) for a node regression task. This talk is based on joint work with Morgane Austern, Kenny Gu, and Somak Laha.