# E(n) Equivariant Message Passing Cellular Networks

arXiv: https://arxiv.org/abs/2406.03145 · HTML: https://mlsanity.com/paper/2406.03145/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 47 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 30 of 30)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space](https://mlsanity.com/paper/2310.02970/) (2023)
- [E(n) Equivariant Message Passing Simplicial Networks](https://mlsanity.com/paper/2305.07100/) (2023)
- [Clifford Group Equivariant Simplicial Message Passing Networks](https://mlsanity.com/paper/2402.10011/) (2024)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [Topo-MLP : A Simplicial Network Without Message Passing](https://mlsanity.com/paper/2312.11862/) (2023)

## Built on by (most cited first, 3 of 3)

- [Controlled Generation with Equivariant Variational Flow Matching](https://mlsanity.com/paper/2506.18340/) (2025)
- [Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs](https://mlsanity.com/paper/2606.00937/) (2026)
- [Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs](https://mlsanity.com/paper/2608.28853/) (2026)

## Abstract (arXiv)

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