E$(n)$ Equivariant Message Passing Simplicial Networks

Floor Eijkelboom, Rob Hesselink, Erik J Bekkers
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:9071-9081, 2023.

Abstract

This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an $\mathrm{E}(n)$ equivariant fashion. EMPSNs simultaneously generalize $\mathrm{E}(n)$ Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks, thereby serving as a proof of concept for combining geometric and topological information in graph learning. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method individually, being on par with state-of-the-art approaches for learning on geometric graphs. Moreover, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-eijkelboom23a, title = {E$(n)$ Equivariant Message Passing Simplicial Networks}, author = {Eijkelboom, Floor and Hesselink, Rob and Bekkers, Erik J}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {9071--9081}, 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/eijkelboom23a/eijkelboom23a.pdf}, url = {https://proceedings.mlr.press/v202/eijkelboom23a.html}, abstract = {This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an $\mathrm{E}(n)$ equivariant fashion. EMPSNs simultaneously generalize $\mathrm{E}(n)$ Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks, thereby serving as a proof of concept for combining geometric and topological information in graph learning. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method individually, being on par with state-of-the-art approaches for learning on geometric graphs. Moreover, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures.} }
Endnote
%0 Conference Paper %T E$(n)$ Equivariant Message Passing Simplicial Networks %A Floor Eijkelboom %A Rob Hesselink %A Erik J Bekkers %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-eijkelboom23a %I PMLR %P 9071--9081 %U https://proceedings.mlr.press/v202/eijkelboom23a.html %V 202 %X This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an $\mathrm{E}(n)$ equivariant fashion. EMPSNs simultaneously generalize $\mathrm{E}(n)$ Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks, thereby serving as a proof of concept for combining geometric and topological information in graph learning. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method individually, being on par with state-of-the-art approaches for learning on geometric graphs. Moreover, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures.
APA
Eijkelboom, F., Hesselink, R. & Bekkers, E.J.. (2023). E$(n)$ Equivariant Message Passing Simplicial Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:9071-9081 Available from https://proceedings.mlr.press/v202/eijkelboom23a.html.

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