Alejandro Ribeiro (UPenn)
Title:
Machine Learning on Large Scale Graphs: Limit Properties of Convolutional Operators on Graphs
Abstract:
Graph neural networks (GNNs) are compositions of convolutional graph filters with pointwise nonlinearities. In this talk we study graph filters and GNNs in sequences of graphs that converge to a graphon. We define graphon filters and graphon neural networks (WNNs) and connect them to graph filters and GNNs through adequate homomorphisms of an underlying common algebra. We show that this shared algebra leads to a shared frequency (Fourier) representation; which we leverage to study convergence of graph filters to graphon filters. Our convergence results imply that we can train GNNs in medium scale graphs that we can later execute in large scale graphs when they share structural properties. We close by discussing applications and the abstract concept of algebraic neural networks.
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