mlsanityData to 7 Oct 2026

Spherical Message Passing for 3D Graph Networks

arXiv 2102.05013 ↗First posted 9 Feb 2021cs.LGcited by 166

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Abstract (arXiv)

We consider representation learning of 3D molecular graphs in which each atom is associated with a spatial position in 3D. This is an under-explored area of research, and a principled message passing framework is currently lacking. In this work, we conduct analyses in the spherical coordinate system (SCS) for the complete identification of 3D graph structures. Based on such observations, we propose the spherical message passing (SMP) as a novel and powerful scheme for 3D molecular learning. SMP dramatically reduces training complexity, enabling it to perform efficiently on large-scale molecules. In addition, SMP is capable of distinguishing almost all molecular structures, and the uncovered cases may not exist in practice. Based on meaningful physically-based representations of 3D information, we further propose the SphereNet for 3D molecular learning. Experimental results demonstrate that the use of meaningful 3D information in SphereNet leads to significant performance improvements in prediction tasks. Our results also demonstrate the advantages of SphereNet in terms of capability, efficiency, and scalability. Our code is publicly available as part of the DIG library (https://github.com/divelab/DIG).

Key facts. Cited by 166 papers in the map (data through 7 Oct 2026). Builds on 40 of its 62 references that are in the map. First posted on arXiv 9 Feb 2021.

Builds on

40 of 62 references.

References · 40

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
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  11. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  12. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
28 more
  1. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  2. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  3. 2019Deep Learning for 3D Point Clouds: A Surveycited by 557
  4. 2020Directional Message Passing for Molecular Graphscited by 556
  5. 2019Graph U-Netscited by 489
  6. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  7. 2019Provably Powerful Graph Networkscited by 385
  8. 2017Large-scale Point Cloud Semantic Segmentation with Superpoint Graphscited by 384
  9. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 307
  10. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  11. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  12. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  13. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  14. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  15. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
  16. 2018Large-Scale Learnable Graph Convolutional Networkscited by 113
  17. 2020Building powerful and equivariant graph neural networks with structural message-passingcited by 95
  18. 2018N-Gram Graph: Simple Unsupervised Representation for Graphs, with Applications to Moleculescited by 93
  19. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  20. 2019Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspectivecited by 73
  21. 2020OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Featurescited by 63
  22. 2018DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applicationscited by 61
  23. 2020Reinforcement Learning for Molecular Design Guided by Quantum Mechanicscited by 51
  24. 2020Advanced Graph and Sequence Neural Networks for Molecular Property Prediction and Drug Discoverycited by 46
  25. 2020Topology-Aware Graph Pooling Networkscited by 44
  26. 2019Point Cloud Oversegmentation with Graph-Structured Deep Metric Learningcited by 42
  27. 2018End-to-End Learning on 3D Protein Structure for Interface Predictioncited by 32
  28. 2020Deep Learning of High-Order Interactions for Protein Interface Predictioncited by 22

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 38; 2023: 43; 2024: 31; 2025: 33; 2026: 18.

166 papers.

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  1. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  2. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  3. 2022GOOD: A Graph Out-of-Distribution Benchmarkcited by 140
  4. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  5. 2021Geometric Deep Learning on Molecular Representationscited by 113
  6. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  7. 2022Generating 3D Molecules for Target Protein Bindingcited by 104
  8. 2022The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalystscited by 95
  9. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
  10. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  11. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  12. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
38 more
  1. 2022One Transformer Can Understand Both 2D & 3D Molecular Datacited by 77
  2. 2022Conditional Antibody Design as 3D Equivariant Graph Translationcited by 75
  3. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  4. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  5. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  6. 2022DiffBP: Generative Diffusion of 3D Molecules for Target Protein Bindingcited by 58
  7. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  8. 2022Learning Hierarchical Protein Representations via Complete 3D Graph Networkscited by 54
  9. 2022Graph-based Molecular Representation Learningcited by 51
  10. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  11. 2021Simple GNN Regularisation for 3D Molecular Property Prediction & Beyondcited by 44
  12. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  13. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  14. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 38
  15. 2022Improving Molecular Contrastive Learning via Faulty Negative Mitigation and Decomposed Fragment Contrastcited by 37
  16. 2022Energy-Motivated Equivariant Pretraining for 3D Molecular Graphscited by 37
  17. 2023Efficient Approximations of Complete Interatomic Potentials for Crystal Property Predictioncited by 37
  18. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  19. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 37
  20. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  21. 2023Fractional Denoising for 3D Molecular Pre-trainingcited by 33
  22. 2022GraphFM: Improving Large-Scale GNN Training via Feature Momentumcited by 31
  23. 2024Cartesian atomic cluster expansion for machine learning interatomic potentialscited by 31
  24. 2023Functional-Group-Based Diffusion for Pocket-Specific Molecule Generation and Elaborationcited by 30
  25. 2021Learning 3D Representations of Molecular Chirality with Invariance to Bond Rotationscited by 29
  26. 2023A Latent Diffusion Model for Protein Structure Generationcited by 28
  27. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  28. 2023Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generationcited by 27
  29. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  30. 2022Towards Training Billion Parameter Graph Neural Networks for Atomic Simulationscited by 25
  31. 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
  32. 2023Towards Symmetry-Aware Generation of Periodic Materialscited by 25
  33. 2023Automated 3D Pre-Training for Molecular Property Predictioncited by 24
  34. 2022Molecular Representation Learning via Heterogeneous Motif Graph Neural Networkscited by 23
  35. 2023Towards Fair Graph Neural Networks via Graph Counterfactualcited by 23
  36. 2023Highly Accurate Quantum Chemical Property Prediction with Uni-Mol+cited by 22
  37. 2022Graph Neural Networks for Moleculescited by 21
  38. 2022FlowX: Towards Explainable Graph Neural Networks via Message Flowscited by 20

50 most cited of 166 All 166 (JSON)