E(n) Equivariant Message Passing Cellular Networks

TL;DR

This paper presents EMPCNs, a novel extension of equivariant graph neural networks to CW-complexes, enhancing expressiveness and efficiency for geometric message passing tasks.

Contribution

It introduces EMPCNs, enabling higher-order message passing on CW-complexes with improved expressiveness and computational efficiency, outperforming previous models in generalization.

Findings

Achieves near state-of-the-art performance on multiple tasks.

Decoupled EMPCNs show stronger generalization.

Effective for higher-order geometric and topological graphs.

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