mlsanityData to 14 Oct 2026

Geometrically Equivariant Graph Neural Networks: A Survey

arXiv 2202.07230 ↗First posted 15 Feb 2022cs.LGcited by 56

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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.

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

42 of 63 references.

References · 42

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2017Inductive Representation Learning on Large Graphscited by 6,320
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  6. 2016Group Equivariant Convolutional Networkscited by 1,165
  7. 2021E(n) Equivariant Graph Neural Networkscited by 965
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  9. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  10. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 680
  11. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  12. 2020Directional Message Passing for Molecular Graphscited by 561
30 more
  1. 2019Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Datacited by 532
  2. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  3. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  4. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  5. 2018Neural Relational Inference for Interacting Systemscited by 339
  6. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  7. 2016Steerable CNNscited by 305
  8. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  9. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
  10. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  11. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 243
  12. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  13. 2018Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluidscited by 220
  14. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  15. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 182
  16. 2021Spherical Message Passing for 3D Graph Networkscited by 168
  17. 2021E(n) Equivariant Normalizing Flowscited by 165
  18. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 163
  19. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  20. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  21. 2020Expressive Power of Invariant and Equivariant Graph Neural Networkscited by 100
  22. 2020LieTransformer: Equivariant self-attention for Lie Groupscited by 100
  23. 2018Flexible Neural Representation for Physics Predictioncited by 91
  24. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 82
  25. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  26. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  27. 2020ATOM3D: Tasks On Molecules in Three Dimensionscited by 74
  28. 2020An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storagecited by 45
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 9; 2023: 22; 2024: 15; 2025: 6; 2026: 4.

56 papers.

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  1. 2022Conditional Antibody Design as 3D Equivariant Graph Translationcited by 75
  2. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
  3. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 68
  4. 2023Clifford Group Equivariant Neural Networkscited by 55
  5. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 39
  6. 2022Energy-Motivated Equivariant Pretraining for 3D Molecular Graphscited by 37
  7. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimizationcited by 37
  8. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  9. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  10. 2022Equivariant Graph Hierarchy-Based Neural Networkscited by 24
  11. 2023Navigating protein landscapes with a machine-learned transferable coarse-grained modelcited by 23
  12. 2023Is Distance Matrix Enough for Geometric Deep Learning?cited by 22
38 more
  1. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  2. 2024E(n) Equivariant Topological Neural Networkscited by 22
  3. 2022Graph Neural Networks for Moleculescited by 21
  4. 2023Scaling Spherical CNNscited by 21
  5. 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 19
  6. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 19
  7. 2022An Analysis of Attention via the Lens of Exchangeability and Latent Variable Modelscited by 16
  8. 2023EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Predictioncited by 15
  9. 2023Lie Group Decompositions for Equivariant Neural Networkscited by 12
  10. 2024RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentationcited by 12
  11. 2023Spatial Attention Kinetic Networks with E(n)-Equivariancecited by 11
  12. 2023Subequivariant Graph Reinforcement Learning in 3D Environmentscited by 11
  13. 2023BeMap: Balanced Message Passing for Fair Graph Neural Networkcited by 11
  14. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  15. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
  16. 2023A Universal Framework for Accurate and Efficient Geometric Deep Learning of Molecular Systemscited by 10
  17. 2024Beyond Sequence: Impact of Geometric Context for RNA Property Predictioncited by 8
  18. 2022SS-GNN: A Simple-Structured Graph Neural Network for Affinity Predictioncited by 7
  19. 2023Multi-task Bioassay Pre-training for Protein-ligand Binding Affinity Predictioncited by 7
  20. 2023CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generationcited by 7
  21. 2023State of the Art and Potentialities of Graph-level Learningcited by 6
  22. 2022PEMP: Leveraging Physics Properties to Enhance Molecular Property Predictioncited by 5
  23. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  24. 2024Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systemscited by 4
  25. 2023DuEqNet: Dual-Equivariance Network in Outdoor 3D Object Detection for Autonomous Drivingcited by 3
  26. 2023Accurate and Definite Mutational Effect Prediction with Lightweight Equivariant Graph Neural Networkscited by 3
  27. 2024Molecule Graph Networks with Many-body Equivariant Interactionscited by 3
  28. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  29. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 3
  30. 2023Geometric Deep Learning for Structure-Based Drug Design: A Surveycited by 2
  31. 2023Docking-based generative approaches in the search for new drug candidatescited by 2
  32. 2024Bridging Geometric States via Geometric Diffusion Bridgecited by 2
  33. 2025GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebrascited by 2
  34. 2025ProtPainter: Draw or Drag Protein via Topology-guided Diffusioncited by 1
  35. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  36. 2022GRAPHYP: A Scientific Knowledge Graph with Manifold Subnetworks of Communities. Detection of Scholarly Disputes in Adversarial Information Routescited by 0
  37. 2024Equivariant Spatio-Temporal Attentive Graph Networks to Simulate Physical Dynamicscited by 0
  38. 2024Improving Molecular Modeling with Geometric GNNs: an Empirical Studycited by 0

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