Directional Graph Networks

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.

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification CIFAR10 100k DGN Accuracy (%) 72.84 # 1
Graph Property Prediction ogbg-molhiv DGN Test ROC-AUC 0.7970 ± 0.0097 # 17
Validation ROC-AUC 0.8470 ± 0.0047 # 5
Number of params 114065 # 32
Ext. data No # 1
Graph Property Prediction ogbg-molpcba DGN Test AP 0.2885 ± 0.0030 # 13
Validation AP 0.2970 ± 0.0021 # 14
Number of params 6732696 # 6
Ext. data No # 1
Node Classification PATTERN 100k DGN Accuracy (%) 86.680 # 2


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