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
@article{arxiv.2406.03145,
title = {E(n) Equivariant Message Passing Cellular Networks},
author = {Veljko Kovač and Erik J. Bekkers and Pietro Liò and Floor Eijkelboom},
journal= {arXiv preprint arXiv:2406.03145},
year = {2024}
}