E(n) Equivariant Message Passing Cellular Networks

• URL: http://arxiv.org/abs/2406.03145v3
• Date: Thu, 18 Jul 2024 08:21:34 GMT
• Title: E(n) Equivariant Message Passing Cellular Networks
• Authors: Veljko Kovač, Erik J. Bekkers, Pietro Liò, Floor Eijkelboom,
• Abstract summary: We introduce E(n) Equivariant Message Passing Cellular Networks (EMPCNs) EMPCNs are an extension of E(n) Equivariant Graph Networks to CW-complexes. We show that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability.
• Score: 21.95746068487803
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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

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