Directional Graph Networks

Dominique Beani, Saro Passaro, Vincent Létourneau, Will Hamilton, Gabriele Corso, Pietro Lió
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:748-758, 2021.

Abstract

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v139-beani21a, title = {Directional Graph Networks}, author = {Beani, Dominique and Passaro, Saro and L{\'e}tourneau, Vincent and Hamilton, Will and Corso, Gabriele and Li{\'o}, Pietro}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {748--758}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/beani21a/beani21a.pdf}, url = {https://proceedings.mlr.press/v139/beani21a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Directional Graph Networks %A Dominique Beani %A Saro Passaro %A Vincent Létourneau %A Will Hamilton %A Gabriele Corso %A Pietro Lió %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-beani21a %I PMLR %P 748--758 %U https://proceedings.mlr.press/v139/beani21a.html %V 139 %X 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.
APA
Beani, D., Passaro, S., Létourneau, V., Hamilton, W., Corso, G. & Lió, P.. (2021). Directional Graph Networks. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:748-758 Available from https://proceedings.mlr.press/v139/beani21a.html.

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