Directional Graph Networks
This addresses a fundamental bottleneck in GNNs for better modeling anisotropic features in physical or biological problems, representing a novel advancement rather than an incremental improvement.
The paper tackled the limitation of isotropic kernels in graph neural networks (GNNs) by proposing the first globally consistent anisotropic kernels, which improved expressiveness and reduced issues like over-smoothing, achieving relative error reductions of 8% on CIFAR10 and 11-32% on ZINC, and a 1.6% precision increase on MolPCBA.
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an $n$-dimensional grid and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. We evaluate our method on different standard benchmarks and see a relative error reduction of 8% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.