Attraction-Repulsion Dynamics versus Homophily in GNNs
2023 · Exploring attraction, repulsion, and graph homophily in the Gradient Flow Framework.
Most established Graph Neural Network architectures rely on the input graphs to be homophilic. On heterophilic graphs, they often perform worse than structure-agnostic models. The recently proposed Gradient Flow Framework (GraFF) generalises many architectures as discretisations of gradient flow differential equations. Governed by the spectrum of one of its channel-mixing matrices, GraFF allows for both attractive and repulsive interactions between node representations in the latent space of a GNN. In this work, we examine the natural relationship between this attraction/repulsion behaviour and the homophily ratio of the input graph. Our findings suggest that this relationship is much weaker than expected.