mlsanityData to 7 Oct 2026

A new perspective on building efficient and expressive 3D equivariant graph neural networks

arXiv 2304.04757 ↗First posted 7 Apr 2023cs.LG cs.AIcited by 46

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Abstract (arXiv)

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these networks through a local-to-global analysis lacks today. In this paper, we propose a local hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs and investigate the process of representing global geometric information from local patches. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs; namely local substructure encoding (LSE) and frame transition encoding (FTE). To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules and achieves state-of-the-art performance on both scalar-valued and vector-valued molecular property prediction tasks. We further point out the design space for future developments of equivariant graph neural networks. Our codes are available at urlhttps://github.com/yuanqidu/LeftNet.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 48 of its 64 references that are in the map. First posted on arXiv 7 Apr 2023.

Builds on

48 of 64 references.

References · 48

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  7. 2017Deep Setscited by 1,394
  8. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  9. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  10. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  11. 2021E(n) Equivariant Graph Neural Networkscited by 951
  12. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
36 more
  1. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  2. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  3. 2020Directional Message Passing for Molecular Graphscited by 556
  4. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  5. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  6. 2019Analyzing Learned Molecular Representations for Property Predictioncited by 373
  7. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  8. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  9. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  10. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  11. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  12. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  13. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  14. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  15. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  16. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 204
  17. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  18. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  19. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
  20. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  21. 2021Geometric Deep Learning on Molecular Representationscited by 113
  22. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  23. 2019Machine learning for molecular simulationcited by 109
  24. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  25. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  26. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  27. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  28. 2021DIG: A Turnkey Library for Diving into Graph Deep Learning Researchcited by 76
  29. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  30. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  31. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  32. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  33. 2022Learning Hierarchical Protein Representations via Complete 3D Graph Networkscited by 54
  34. 2020Advanced Graph and Sequence Neural Networks for Molecular Property Prediction and Drug Discoverycited by 46
  35. 2022Equivariant Graph Attention Networks for Molecular Property Predictioncited by 19
  36. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 8; 2024: 14; 2025: 12; 2026: 12.

46 papers.

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  1. 2023Equivariant flow matchingcited by 131
  2. 2024Transferable Boltzmann Generatorscited by 43
  3. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  4. 2023A Group Symmetric Stochastic Differential Equation Model for Molecule Multi-modal Pretrainingcited by 32
  5. 2023Accurate transition state generation with an object-aware equivariant elementary reaction diffusion modelcited by 30
  6. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  7. 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
  8. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  9. 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 18
  10. 2024Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passingcited by 13
  11. 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
  12. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
34 more
  1. 2023Molecule Joint Auto-Encoding: Trajectory Pretraining with 2D and 3D Diffusioncited by 10
  2. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  3. 2023Learning Over Molecular Conformer Ensembles: Datasets and Benchmarkscited by 9
  4. 2025MolSpectra: Pre-training 3D Molecular Representation with Multi-modal Energy Spectracited by 8
  5. 2024On the Expressive Power of Sparse Geometric MPNNscited by 7
  6. 2025MatLLMSearch: Crystal Structure Discovery with Evolution-Guided Large Language Modelscited by 7
  7. 2024Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Predictioncited by 6
  8. 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
  9. 2026MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentialscited by 6
  10. 2024Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networkscited by 4
  11. 2025Building-Block Aware Generative Modeling for 3D Crystals of Metal Organic Frameworkscited by 4
  12. 2025Geometric Hyena Networks for Large-scale Equivariant Learningcited by 4
  13. 2024React-OT: Optimal Transport for Generating Transition State in Chemical Reactionscited by 3
  14. 2025Group Downsampling with Equivariant Anti-aliasingcited by 3
  15. 2024SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learningcited by 2
  16. 2025AlphaNet: Scaling Up Local-frame-based Atomistic Interatomic Potentialcited by 2
  17. 2025Tokenizing Electron Cloud in Protein-Ligand Interaction Learningcited by 2
  18. 2025Topotein: Topological Deep Learning for Protein Representation Learningcited by 2
  19. 2026FragmentFlow: Scalable Transition State Generation for Large Moleculescited by 2
  20. 2026A Cross-Domain Graph Learning Protocol for Single-Step Molecular Geometry Refinementcited by 1
  21. 2024A quatum inspired neural network for geometric modelingcited by 0
  22. 2024Geometric Self-Supervised Pretraining on 3D Protein Structures using Subgraphscited by 0
  23. 2025CrystalFramer: Rethinking the Role of Frames for SE(3)-Invariant Crystal Structure Modelingcited by 0
  24. 2025ModuLM: Enabling Modular and Multimodal Molecular Relational Learning with Large Language Modelscited by 0
  25. 2025A Single Architecture for Representing Invariance Under Any Space Groupcited by 0
  26. 2026Towards Multiscale Graph-based Protein Learning with Geometric Secondary Structural Motifscited by 0
  27. 2026GDEGAN: Gaussian Dynamic Equivariant Graph Attention Network for Ligand Binding Site Predictioncited by 0
  28. 2026Tunable Soft Equivariance with Guaranteescited by 0
  29. 2026h-MINT: Modeling Pocket-Ligand Binding with Hierarchical Molecular Interaction Networkcited by 0
  30. 2026Benchmarking bandgap prediction in semiconductors under experimental and realistic evaluation settingscited by 0
  31. 2026Curvature-Informed Potential Energy Surface for Protein-Ligand Binding Affinity Predictioncited by 0
  32. 2026Reaction-Transformation-Aware Flow Matching for Generalizable Transition State Generationcited by 0
  33. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0
  34. 2026Rotational Equivariance in Machine Learning: A Comprehensive Tutorialcited by 0