2021-07-01-beaini21a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
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.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	beani21a	0	Directional Graph Networks	748	758	748-758	748	false	Beaini, Dominique and Passaro, Saro and L{\'e}tourneau, Vincent and Hamilton, Will and Corso, Gabriele and Li{\'o}, Pietro	given family Dominique Beaini given family Saro Passaro given family Vincent Létourneau given family Will Hamilton given family Gabriele Corso given family Pietro Lió	2021-07-01		Proceedings of the 38th International Conference on Machine Learning	139	inproceedings	date-parts 2021 7 1	http://proceedings.mlr.press/v139/beaini21a/beaini21a.pdf	label link Supplementary PDF http://proceedings.mlr.press/v139/beaini21a/beaini21a-supp.pdf