E(n) Equivariant Message Passing Cellular Networks

Veljko Kovac̆, Erik Bekkers, Pietro Lió, Floor Eijkelboom
Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), PMLR 251:173-186, 2024.

Abstract

This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1) enhancing their expressiveness by incorporating arbitrary cells, and 2) achieving this in a computationally efficient way with a decoupled EMPCNs technique. We demonstrate that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability, including many-body predictions and motion capture. Moreover, ablation studies confirm that decoupled EMPCNs exhibit stronger generalization capabilities than their non-topologically informed counterparts. These findings show that EMPCNs can be used as a scalable and expressive framework for higher-order message passing in geometric and topological graphs

Cite this Paper

BibTeX
@InProceedings{pmlr-v251-kovac-24a, title = {E(n) Equivariant Message Passing Cellular Networks}, author = {Kova\u{c}, Veljko and Bekkers, Erik and Li\'{o}, Pietro and Eijkelboom, Floor}, booktitle = {Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM)}, pages = {173--186}, year = {2024}, editor = {Vadgama, Sharvaree and Bekkers, Erik and Pouplin, Alison and Kaba, Sekou-Oumar and Walters, Robin and Lawrence, Hannah and Emerson, Tegan and Kvinge, Henry and Tomczak, Jakub and Jegelka, Stephanie}, volume = {251}, series = {Proceedings of Machine Learning Research}, month = {29 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v251/main/assets/kovac-24a/kovac-24a.pdf}, url = {https://proceedings.mlr.press/v251/kovac-24a.html}, abstract = {This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1) enhancing their expressiveness by incorporating arbitrary cells, and 2) achieving this in a computationally efficient way with a decoupled EMPCNs technique. We demonstrate that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability, including many-body predictions and motion capture. Moreover, ablation studies confirm that decoupled EMPCNs exhibit stronger generalization capabilities than their non-topologically informed counterparts. These findings show that EMPCNs can be used as a scalable and expressive framework for higher-order message passing in geometric and topological graphs} }
Endnote
%0 Conference Paper %T E(n) Equivariant Message Passing Cellular Networks %A Veljko Kovac̆ %A Erik Bekkers %A Pietro Lió %A Floor Eijkelboom %B Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) %C Proceedings of Machine Learning Research %D 2024 %E Sharvaree Vadgama %E Erik Bekkers %E Alison Pouplin %E Sekou-Oumar Kaba %E Robin Walters %E Hannah Lawrence %E Tegan Emerson %E Henry Kvinge %E Jakub Tomczak %E Stephanie Jegelka %F pmlr-v251-kovac-24a %I PMLR %P 173--186 %U https://proceedings.mlr.press/v251/kovac-24a.html %V 251 %X This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1) enhancing their expressiveness by incorporating arbitrary cells, and 2) achieving this in a computationally efficient way with a decoupled EMPCNs technique. We demonstrate that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability, including many-body predictions and motion capture. Moreover, ablation studies confirm that decoupled EMPCNs exhibit stronger generalization capabilities than their non-topologically informed counterparts. These findings show that EMPCNs can be used as a scalable and expressive framework for higher-order message passing in geometric and topological graphs
APA
Kovac̆, V., Bekkers, E., Lió, P. & Eijkelboom, F.. (2024). E(n) Equivariant Message Passing Cellular Networks. Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM), in Proceedings of Machine Learning Research 251:173-186 Available from https://proceedings.mlr.press/v251/kovac-24a.html.

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