E(n) Equivariant Message Passing Cellular Networks
<|reference_start|>E(n) Equivariant Message Passing Cellular Networks: 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<|reference_end|>
@article{kovač2024e(n),
    title={E(n) Equivariant Message Passing Cellular Networks},
    author={Veljko Kovav{c}, Erik J. Bekkers, Pietro Li`o, Floor Eijkelboom},
    journal={arXiv preprint arXiv:2406.03145},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03145},
    primaryClass={cs.LG}
}