# E(n) Equivariant Message Passing Simplicial Networks

arXiv: https://arxiv.org/abs/2305.07100 · HTML: https://mlsanity.com/paper/2305.07100/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 25 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (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)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [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)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [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)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Latent-Graph Learning for Disease Prediction](https://mlsanity.com/paper/2003.13620/) (2020)
- [Iterative SE(3)-Transformers](https://mlsanity.com/paper/2102.13419/) (2021)

## Built on by (most cited first, 23 of 23)

- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [Clifford Group Equivariant Simplicial Message Passing Networks](https://mlsanity.com/paper/2402.10011/) (2024)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Grounding Continuous Representations in Geometry: Equivariant Neural Fields](https://mlsanity.com/paper/2406.05753/) (2024)
- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [Graph Neural PDE Solvers with Conservation and Similarity-Equivariance](https://mlsanity.com/paper/2405.16183/) (2024)
- [Topological Neural Networks go Persistent, Equivariant, and Continuous](https://mlsanity.com/paper/2406.03164/) (2024)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [Controlled Generation with Equivariant Variational Flow Matching](https://mlsanity.com/paper/2506.18340/) (2025)
- [Higher-Order Topological Directionality and Directed Simplicial Neural Networks](https://mlsanity.com/paper/2409.08389/) (2024)
- [A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networks](https://mlsanity.com/paper/2410.04692/) (2024)
- [E(n) Equivariant Message Passing Cellular Networks](https://mlsanity.com/paper/2406.03145/) (2024)
- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks](https://mlsanity.com/paper/2605.00725/) (2026)
- [Geometry-Aware Simplicial Message Passing](https://mlsanity.com/paper/2605.06061/) (2026)
- [Augmented Equivariant Mesh Networks for Anatomical Segmentation](https://mlsanity.com/paper/2605.08172/) (2026)
- [Hypergraph Pattern Machine: Compositional Tokenization for Higher-Order Interactions](https://mlsanity.com/paper/2605.16527/) (2026)
- [A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of O(2)](https://mlsanity.com/paper/2606.27864/) (2026)
- [Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operators](https://mlsanity.com/paper/2609.05860/) (2026)
- [Clifford Sheaf Neural Networks](https://mlsanity.com/paper/2610.01322/) (2026)

## Abstract (arXiv)

This paper presents E(n) Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an E(n) equivariant fashion. EMPSNs simultaneously generalize E(n) Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method. Furthermore, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures. Last, we show that EMPSNs are on par with state-of-the-art approaches for learning on geometric graphs.