mlsanityData to 7 Oct 2026

3D-Rotation-Equivariant Quaternion Neural Networks

arXiv 1911.09040 ↗First posted 20 Nov 2019cs.CV cs.LG stat.MLcited by 30

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Abstract (arXiv)

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rotation equivariance means that applying a specific rotation transformation to the input point cloud is equivalent to applying the same rotation transformation to all intermediate-layer quaternion features. Besides, the REQNN also ensures that the intermediate-layer features are invariant to the permutation of input points. Compared with the original neural network, the REQNN exhibits higher rotation robustness.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Nov 2019.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 5; 2024: 6; 2025: 3; 2026: 3.

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  1. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  2. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  3. 20223D Equivariant Graph Implicit Functionscited by 18
  4. 2021Interpreting Representation Quality of DNNs for 3D Point Cloud Processingcited by 12
  5. 2022ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotationcited by 12
  6. 2022SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representationcited by 10
  7. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  8. 2021Adjoint Rigid Transform Network: Task-conditioned Alignment of 3D Shapescited by 4
  9. 2024MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysiscited by 4
  10. 2023Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learningcited by 3
  11. 2023Quaternion Convolutional Neural Networks: Current Advances and Future Directionscited by 3
  12. 2024Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagationcited by 3
18 more
  1. 2024Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transformcited by 3
  2. 2021Rotation Transformation Network: Learning View-Invariant Point Cloud for Classification and Segmentationcited by 2
  3. 2022TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysiscited by 2
  4. 2023General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignmentcited by 2
  5. 2023Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillationcited by 2
  6. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  7. 2025SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spherescited by 2
  8. 2025Learning Generalizable Shape Completion with SIM(3) Equivariancecited by 2
  9. 2022PointTree: Transformation-Robust Point Cloud Encoder with Relaxed K-D Treescited by 1
  10. 2022SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancementcited by 1
  11. 2023VNI-Net: Vector Neurons-based Rotation-Invariant Descriptor for LiDAR Place Recognitioncited by 1
  12. 2024View Transformation Robustness for Multi-View 3D Object Reconstruction with Reconstruction Error-Guided View Selectioncited by 1
  13. 2025RotaTouille: Rotation Equivariant Deep Learning for Contourscited by 1
  14. 2022Design equivariant neural networks for 3D point cloudcited by 0
  15. 2022Quaternion Backpropagationcited by 0
  16. 2026REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformercited by 0
  17. 2026Encoding the Euler Characteristic Transformcited by 0
  18. 2026QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Latticescited by 0