mlsanityData to 7 Oct 2026

Equivariant Point Cloud Analysis via Learning Orientations for Message Passing

arXiv 2203.14486 ↗First posted 28 Mar 2022cs.CVcited by 32

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Abstract (arXiv)

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decouple the relative position for each point from the global pose of the entire point cloud. Therefore, we extend current message passing networks with a module that learns orientations for each point. Before aggregating information from the neighbors of a point, the networks transforms the neighbors' coordinates based on the point's learned orientations. We provide formal proofs to show the equivariance of the proposed framework. Empirically, we demonstrate that our proposed method is competitive on both point cloud analysis and physical modeling tasks. Code is available at https://github.com/luost26/Equivariant-OrientedMP .

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). Builds on 32 of its 48 references that are in the map. First posted on arXiv 28 Mar 2022.

Builds on

32 of 48 references.

References · 32

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  5. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  6. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  7. 2018On the Continuity of Rotation Representations in Neural Networkscited by 1,186
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2018PointCNN: Convolution On X-Transformed Pointscited by 764
  10. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  11. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  12. 2018PointConv: Deep Convolutional Networks on 3D Point Cloudscited by 656
20 more
  1. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  2. 2020Directional Message Passing for Molecular Graphscited by 556
  3. 2019Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimationcited by 490
  4. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  5. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  6. 2019Relation-Shape Convolutional Neural Network for Point Cloud Analysiscited by 346
  7. 2018Neural Relational Inference for Interacting Systemscited by 339
  8. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  9. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  10. 2018PPFNet: Global Context Aware Local Features for Robust 3D Point Matchingcited by 180
  11. 2019Category-Level Articulated Object Pose Estimationcited by 158
  12. 2019ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statisticscited by 104
  13. 2019Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 80
  14. 2018Unsupervised Geometry-Aware Representation for 3D Human Pose Estimationcited by 73
  15. 2020A Rotation-Invariant Framework for Deep Point Cloud Analysiscited by 62
  16. 2019Quaternion Equivariant Capsule Networks for 3D Point Cloudscited by 41
  17. 2020Canonical Capsules: Self-Supervised Capsules in Canonical Posecited by 30
  18. 2020Global Context Aware Convolutions for 3D Point Cloud Understandingcited by 26
  19. 2018Momen(e)t: Flavor the Moments in Learning to Classify Shapescited by 15
  20. 2019Rotation Invariant Point Cloud Classification: Where Local Geometry Meets Global Topologycited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 7; 2024: 9; 2025: 9; 2026: 1.

32 papers.

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  1. 2022Equivariance with Learned Canonicalization Functionscited by 106
  2. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 104
  3. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  4. 2024RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learningcited by 15
  5. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
  6. 2023Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariancecited by 14
  7. 2024Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passingcited by 13
  8. 2022NeuralBF: Neural Bilateral Filtering for Top-down Instance Segmentation on Point Cloudscited by 12
  9. 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
  10. 2023Equivariant Neural Operator Learning with Graphon Convolutioncited by 10
  11. 2023PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restorationcited by 7
  12. 2023Latent Field Discovery In Interacting Dynamical Systems With Neural Fieldscited by 7
20 more
  1. 2024Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysiscited by 6
  2. 2022Rethinking Rotation Invariance with Point Cloud Registrationcited by 5
  3. 2025Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learningcited by 5
  4. 2024MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysiscited by 4
  5. 2023Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learningcited by 3
  6. 2024Geometric Point Attention Transformer for 3D Shape Reassemblycited by 3
  7. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  8. 2022TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysiscited by 2
  9. 2023Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillationcited by 2
  10. 2024Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondencecited by 2
  11. 2024Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environmentscited by 2
  12. 2025Combinative Matching for Geometric Shape Assemblycited by 2
  13. 2025Towards a 3D Transfer-based Black-box Attack via Critical Feature Guidancecited by 2
  14. 2023Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbitscited by 1
  15. 2024Point-PNG: Conditional Pseudo-Negatives Generation for Point Cloud Pre-Trainingcited by 1
  16. 2025HFBRI-MAE: Handcrafted Feature Based Rotation-Invariant Masked Autoencoder for 3D Point Cloud Analysiscited by 1
  17. 2025Frame-based Equivariant Diffusion Models for 3D Molecular Generationcited by 1
  18. 2025Stable and Accurate Orbital-Free DFT Powered by Machine Learningcited by 0
  19. 2025Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learningcited by 0
  20. 2026Rotational Equivariance in Machine Learning: A Comprehensive Tutorialcited by 0