# Geometrically Equivariant Graph Neural Networks: A Survey

arXiv: https://arxiv.org/abs/2202.07230 · HTML: https://mlsanity.com/paper/2202.07230/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 63 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [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)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [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)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)

## Built on by (most cited first, 30 of 56)

- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Learning Physical Dynamics with Subequivariant Graph Neural Networks](https://mlsanity.com/paper/2210.06876/) (2022)
- [Energy-Motivated Equivariant Pretraining for 3D Molecular Graphs](https://mlsanity.com/paper/2207.08824/) (2022)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products](https://mlsanity.com/paper/2401.10216/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Equivariant Graph Hierarchy-Based Neural Networks](https://mlsanity.com/paper/2202.10643/) (2022)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Is Distance Matrix Enough for Geometric Deep Learning?](https://mlsanity.com/paper/2302.05743/) (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)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Scaling Spherical CNNs](https://mlsanity.com/paper/2306.05420/) (2023)
- [Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning](https://mlsanity.com/paper/2306.01474/) (2023)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [An Analysis of Attention via the Lens of Exchangeability and Latent Variable Models](https://mlsanity.com/paper/2212.14852/) (2022)
- [EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Prediction](https://mlsanity.com/paper/2302.12177/) (2023)
- [Lie Group Decompositions for Equivariant Neural Networks](https://mlsanity.com/paper/2310.11366/) (2023)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [Spatial Attention Kinetic Networks with E(n)-Equivariance](https://mlsanity.com/paper/2301.08893/) (2023)
- [Subequivariant Graph Reinforcement Learning in 3D Environments](https://mlsanity.com/paper/2305.18951/) (2023)
- [BeMap: Balanced Message Passing for Fair Graph Neural Network](https://mlsanity.com/paper/2306.04107/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [On the Completeness of Invariant Geometric Deep Learning Models](https://mlsanity.com/paper/2402.04836/) (2024)
- [A Universal Framework for Accurate and Efficient Geometric Deep Learning of Molecular Systems](https://mlsanity.com/paper/2311.11228/) (2023)
- [Beyond Sequence: Impact of Geometric Context for RNA Property Prediction](https://mlsanity.com/paper/2410.11933/) (2024)
- [SS-GNN: A Simple-Structured Graph Neural Network for Affinity Prediction](https://mlsanity.com/paper/2206.07015/) (2022)

## Abstract (arXiv)

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias and developed geometrically equivariant Graph Neural Networks (GNNs) to better characterize the geometry and topology of geometric graphs. Despite fruitful achievements, it still lacks a survey to depict how equivariant GNNs are progressed, which in turn hinders the further development of equivariant GNNs. To this end, based on the necessary but concise mathematical preliminaries, we analyze and classify existing methods into three groups regarding how the message passing and aggregation in GNNs are represented. We also summarize the benchmarks as well as the related datasets to facilitate later researches for methodology development and experimental evaluation. The prospect for future potential directions is also provided.