Curvature Filtrations for Graph Generative Model Evaluation

Joshua Southern, Jeremy Wayland, Michael M. Bronstein, Bastian Rieck

Keywords: Curvature, topology, persistent homology, graph learning, generative model, machine learning, geometric deep learning

TL;DR: We present a stable, expressive, and scalable method for graph generative model evaluation based on discrete curvature and topological data analysis.

Abstract: Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property of graphs, and has recently started to prove useful in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

Submission Number: 6763