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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks

February 1, 2023

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Authors

Christopher Morris

TU Dortmund University


Martin Ritzert

RWTH Aachen University


Matthias Fey

TU Dortmund University


William L. Hamilton

Stanford University


Jan Eric Lenssen

TU Dortmund University


Gaurav Rattan

RWTH Aachen University


Martin Grohe

RWTH Aachen University


DOI:

10.1609/aaai.v33i01.33014602


Abstract:

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically—showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

Topics: AAAI

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HOW TO CITE:

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks Proceedings of the AAAI Conference on Artificial Intelligence (2019) 4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks AAAI 2019, 4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe (2019). Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. 2019. Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. "Proceedings of the AAAI Conference on Artificial Intelligence". 4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. (2019) "Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks", Proceedings of the AAAI Conference on Artificial Intelligence, p.4602-4609

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe, "Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks", AAAI, p.4602-4609, 2019.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. "Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. "Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 4602-4609.

Christopher Morris||Martin Ritzert||Matthias Fey||William L. Hamilton||Jan Eric Lenssen||Gaurav Rattan||Martin Grohe. Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. AAAI[Internet]. 2019[cited 2023]; 4602-4609.


ISSN: 2374-3468


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