Papers › Directional Graph Networks

Directional Graph Networks

6 Oct 2020arXiv:2010.02863archive 2025-07-28

Dominique Beaini, Saro Passaro, Vincent Létourneau, William L. Hamilton, Gabriele Corso, Pietro Liò

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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get_activation gbouritsas/gsn/directional_gsn/nets/layers.py community (archive-listed) ran · our draft was wrong MIT (permissive) · fe76e55f0b804b7b · report
gpu_setup gbouritsas/gsn/directional_gsn/main_HIV.py community (archive-listed) ran · our draft was wrong MIT (permissive) · f72434c0dcd5d11b · report
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str2ListOfLists2int gbouritsas/gsn/directional_gsn/utils_parsing.py community (archive-listed) unverified MIT (permissive) · 94c293b9defb4188 · report
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to_undirected gbouritsas/gsn/directional_gsn/utils_graph_processing.py community (archive-listed) unverified MIT (permissive) · 77a61130d1c9fd6b · report

Tasks

Data AugmentationGraph ClassificationGraph RegressionNode Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Graph Classification CIFAR10 100k DGN Accuracy (%) 72.84 #10 of 20 Archive leaderboard report
Graph Property Prediction ogbg-molhiv DGN Ext. data No #21 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv DGN Number of params 114065 #21 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv DGN Test ROC-AUC 0.7970 ± 0.0097 #21 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv DGN Validation ROC-AUC 0.8470 ± 0.0047 #21 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molpcba DGN Ext. data No #21 of 36 Archive leaderboard report
Graph Property Prediction ogbg-molpcba DGN Number of params 6732696 #21 of 36 Archive leaderboard report
Graph Property Prediction ogbg-molpcba DGN Test AP 0.2885 ± 0.0030 #21 of 36 Archive leaderboard report
Graph Property Prediction ogbg-molpcba DGN Validation AP 0.2970 ± 0.0021 #21 of 36 Archive leaderboard report
Node Classification PATTERN 100k DGN Accuracy (%) 86.680 #2 of 9 Archive leaderboard report

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