The Expressive Power of Path-Based Graph Neural Networks

Caterina Graziani, Tamara Drucks, Fabian Jogl, Monica Bianchini, Franco Scarselli, Thomas Gärtner
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:16226-16249, 2024.

Abstract

We systematically investigate the expressive power of path-based graph neural networks. While it has been shown that path-based graph neural networks can achieve strong empirical results, an investigation into their expressive power is lacking. Therefore, we propose PATH-WL, a general class of color refinement algorithms based on paths and shortest path distance information. We show that PATH-WL is incomparable to a wide range of expressive graph neural networks, can count cycles, and achieves strong empirical results on the notoriously difficult family of strongly regular graphs. Our theoretical results indicate that PATH-WL forms a new hierarchy of highly expressive graph neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-graziani24a, title = {The Expressive Power of Path-Based Graph Neural Networks}, author = {Graziani, Caterina and Drucks, Tamara and Jogl, Fabian and Bianchini, Monica and Scarselli, Franco and G\"{a}rtner, Thomas}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {16226--16249}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/graziani24a/graziani24a.pdf}, url = {https://proceedings.mlr.press/v235/graziani24a.html}, abstract = {We systematically investigate the expressive power of path-based graph neural networks. While it has been shown that path-based graph neural networks can achieve strong empirical results, an investigation into their expressive power is lacking. Therefore, we propose PATH-WL, a general class of color refinement algorithms based on paths and shortest path distance information. We show that PATH-WL is incomparable to a wide range of expressive graph neural networks, can count cycles, and achieves strong empirical results on the notoriously difficult family of strongly regular graphs. Our theoretical results indicate that PATH-WL forms a new hierarchy of highly expressive graph neural networks.} }
Endnote
%0 Conference Paper %T The Expressive Power of Path-Based Graph Neural Networks %A Caterina Graziani %A Tamara Drucks %A Fabian Jogl %A Monica Bianchini %A Franco Scarselli %A Thomas Gärtner %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-graziani24a %I PMLR %P 16226--16249 %U https://proceedings.mlr.press/v235/graziani24a.html %V 235 %X We systematically investigate the expressive power of path-based graph neural networks. While it has been shown that path-based graph neural networks can achieve strong empirical results, an investigation into their expressive power is lacking. Therefore, we propose PATH-WL, a general class of color refinement algorithms based on paths and shortest path distance information. We show that PATH-WL is incomparable to a wide range of expressive graph neural networks, can count cycles, and achieves strong empirical results on the notoriously difficult family of strongly regular graphs. Our theoretical results indicate that PATH-WL forms a new hierarchy of highly expressive graph neural networks.
APA
Graziani, C., Drucks, T., Jogl, F., Bianchini, M., Scarselli, F. & Gärtner, T.. (2024). The Expressive Power of Path-Based Graph Neural Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:16226-16249 Available from https://proceedings.mlr.press/v235/graziani24a.html.

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