# 3D-Rotation-Equivariant Quaternion Neural Networks

arXiv: https://arxiv.org/abs/1911.09040 · HTML: https://mlsanity.com/paper/1911.09040/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 30 of 30)

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [3D Equivariant Graph Implicit Functions](https://mlsanity.com/paper/2203.17178/) (2022)
- [Interpreting Representation Quality of DNNs for 3D Point Cloud Processing](https://mlsanity.com/paper/2111.03549/) (2021)
- [ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotation](https://mlsanity.com/paper/2203.03888/) (2022)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networks](https://mlsanity.com/paper/2410.04692/) (2024)
- [Adjoint Rigid Transform Network: Task-conditioned Alignment of 3D Shapes](https://mlsanity.com/paper/2102.01161/) (2021)
- [MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysis](https://mlsanity.com/paper/2403.00206/) (2024)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation](https://mlsanity.com/paper/2403.11722/) (2024)
- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [Rotation Transformation Network: Learning View-Invariant Point Cloud for Classification and Segmentation](https://mlsanity.com/paper/2107.03105/) (2021)
- [TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis](https://mlsanity.com/paper/2211.14456/) (2022)
- [General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignment](https://mlsanity.com/paper/2302.09907/) (2023)
- [Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillation](https://mlsanity.com/paper/2308.04725/) (2023)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres](https://mlsanity.com/paper/2503.09456/) (2025)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [PointTree: Transformation-Robust Point Cloud Encoder with Relaxed K-D Trees](https://mlsanity.com/paper/2208.05962/) (2022)
- [SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancement](https://mlsanity.com/paper/2211.08250/) (2022)
- [VNI-Net: Vector Neurons-based Rotation-Invariant Descriptor for LiDAR Place Recognition](https://mlsanity.com/paper/2308.12870/) (2023)
- [View Transformation Robustness for Multi-View 3D Object Reconstruction with Reconstruction Error-Guided View Selection](https://mlsanity.com/paper/2412.11428/) (2024)
- [RotaTouille: Rotation Equivariant Deep Learning for Contours](https://mlsanity.com/paper/2508.16359/) (2025)
- [Design equivariant neural networks for 3D point cloud](https://mlsanity.com/paper/2205.00630/) (2022)
- [Quaternion Backpropagation](https://mlsanity.com/paper/2212.13082/) (2022)
- [REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer](https://mlsanity.com/paper/2601.08558/) (2026)
- [Encoding the Euler Characteristic Transform](https://mlsanity.com/paper/2606.10824/) (2026)
- [QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Lattices](https://mlsanity.com/paper/2609.30592/) (2026)

## 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.