Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks

Cristian Bodnar*, Fabrizio Frasca*, Yu Guang Wang*, Nina Otter, Guido Montúfar, Pietro Liò, Michael M. Bronstein

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

85 Scopus citations

Abstract

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs). To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks (GNNs) with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline.

Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Pages1026-1037
Number of pages12
ISBN (Electronic)9781713845065
StatePublished - 2021
Externally publishedYes
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: 18 Jul 202124 Jul 2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Electronic)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online
Period18/07/2124/07/21

Funding

FundersFunder number
EU's Horizon 2020 programme
EU’s Horizon 2020 programme757983, 724228
Teodora Stoleru
European Research Council

    Fingerprint

    Dive into the research topics of 'Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks'. Together they form a unique fingerprint.

    Cite this