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Directional Graph Networks
Dominique Beaini · Saro Passaro · Vincent Létourneau · Will Hamilton · Gabriele Corso · Pietro Lió

Tue Jul 20 09:00 AM -- 11:00 AM (PDT) @ Virtual #None
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.

Author Information

Dominique Beaini (InVivo AI)
Saro Passaro (University of Cambridge)
Vincent Létourneau (Université de Ottawa)
Will Hamilton (McGill University and Mila)
Gabriele Corso (University of Cambridge)
Pietro Lió (University of Cambridge)

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