Local Vertex Colouring Graph Neural Networks

Shouheng Li, Dongwoo Kim, Qing Wang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:19616-19637, 2023.

Abstract

In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in expressivity, they have frequently come at the expense of decreased efficiency or have been restricted to specific types of graphs. In this study, we investigate the expressivity of GNNs from the perspective of graph search. Specifically, we propose a new vertex colouring scheme and demonstrate that classical search algorithms can efficiently compute graph representations that extend beyond the 1-WL. We show the colouring scheme inherits useful properties from graph search that can help solve problems like graph biconnectivity. Furthermore, we show that under certain conditions, the expressivity of GNNs increases hierarchically with the radius of the search neighbourhood. To further investigate the proposed scheme, we develop a new type of GNN based on two search strategies, breadth-first search and depth-first search, highlighting the graph properties they can capture on top of 1-WL. Our code is available at https://github.com/seanli3/lvc.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-li23n, title = {Local Vertex Colouring Graph Neural Networks}, author = {Li, Shouheng and Kim, Dongwoo and Wang, Qing}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {19616--19637}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/li23n/li23n.pdf}, url = {https://proceedings.mlr.press/v202/li23n.html}, abstract = {In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in expressivity, they have frequently come at the expense of decreased efficiency or have been restricted to specific types of graphs. In this study, we investigate the expressivity of GNNs from the perspective of graph search. Specifically, we propose a new vertex colouring scheme and demonstrate that classical search algorithms can efficiently compute graph representations that extend beyond the 1-WL. We show the colouring scheme inherits useful properties from graph search that can help solve problems like graph biconnectivity. Furthermore, we show that under certain conditions, the expressivity of GNNs increases hierarchically with the radius of the search neighbourhood. To further investigate the proposed scheme, we develop a new type of GNN based on two search strategies, breadth-first search and depth-first search, highlighting the graph properties they can capture on top of 1-WL. Our code is available at https://github.com/seanli3/lvc.} }
Endnote
%0 Conference Paper %T Local Vertex Colouring Graph Neural Networks %A Shouheng Li %A Dongwoo Kim %A Qing Wang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-li23n %I PMLR %P 19616--19637 %U https://proceedings.mlr.press/v202/li23n.html %V 202 %X In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in expressivity, they have frequently come at the expense of decreased efficiency or have been restricted to specific types of graphs. In this study, we investigate the expressivity of GNNs from the perspective of graph search. Specifically, we propose a new vertex colouring scheme and demonstrate that classical search algorithms can efficiently compute graph representations that extend beyond the 1-WL. We show the colouring scheme inherits useful properties from graph search that can help solve problems like graph biconnectivity. Furthermore, we show that under certain conditions, the expressivity of GNNs increases hierarchically with the radius of the search neighbourhood. To further investigate the proposed scheme, we develop a new type of GNN based on two search strategies, breadth-first search and depth-first search, highlighting the graph properties they can capture on top of 1-WL. Our code is available at https://github.com/seanli3/lvc.
APA
Li, S., Kim, D. & Wang, Q.. (2023). Local Vertex Colouring Graph Neural Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:19616-19637 Available from https://proceedings.mlr.press/v202/li23n.html.

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