Twitter, Inc. (delisted)
GRAPH NEURAL DIFFUSION

Abstract:

Improved graph neural networks (GNNs) include defining a GNN architecture based on a discretized non-Euclidean diffusion partial differential equation (PDE) such that evolution of feature coordinates represents message passing layers in a GNN and evolution of positional coordinates represents graph rewiring. The GNN being based on both position and feature coordinates has their evolution derived from Beltrami flow. The Beltrami flow is modeled using a Laplace-Beltrami operator, which is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and on Riemannian manifolds. The discretization of the spatial component of the Beltrami flow offers a principled view on positional encoding and graph rewiring, whereas the discretization of the temporal component can replace GNN layers with more flexible adaptive numerical schemes. Based on this model, Beltrami Neural Diffusion (BLEND) that generalizes a broad range of GNN architectures is introduced; BLEND shows state-of-the-art performance on many benchmarks.