# REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer

arXiv: https://arxiv.org/abs/2601.08558 · HTML: https://mlsanity.com/paper/2601.08558/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Cascaded Refinement Network for Point Cloud Completion](https://mlsanity.com/paper/2004.03327/) (2020)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [AdaPoinTr: Diverse Point Cloud Completion with Adaptive Geometry-Aware Transformers](https://mlsanity.com/paper/2301.04545/) (2023)
- [PMP-Net++: Point Cloud Completion by Transformer-Enhanced Multi-step Point Moving Paths](https://mlsanity.com/paper/2202.09507/) (2022)
- [Meta Architecture for Point Cloud Analysis](https://mlsanity.com/paper/2211.14462/) (2022)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)
- [3D Equivariant Graph Implicit Functions](https://mlsanity.com/paper/2203.17178/) (2022)
- [Endowing Deep 3D Models with Rotation Invariance Based on Principal Component Analysis](https://mlsanity.com/paper/1910.08901/) (2019)
- [SCARP: 3D Shape Completion in ARbitrary Poses for Improved Grasping](https://mlsanity.com/paper/2301.07213/) (2023)
- [CRIN: Rotation-Invariant Point Cloud Analysis and Rotation Estimation via Centrifugal Reference Frame](https://mlsanity.com/paper/2303.03101/) (2023)
- [ESCAPE: Equivariant Shape Completion via Anchor Point Encoding](https://mlsanity.com/paper/2412.00952/) (2024)

## Abstract (arXiv)

Incomplete point clouds captured by 3D sensors often result in the loss of both geometric and semantic information. Most existing point cloud completion methods are built on rotation-variant frameworks trained with data in canonical poses, limiting their applicability in real-world scenarios. While data augmentation with random rotations can partially mitigate this issue, it significantly increases the learning burden and still fails to guarantee robust performance under arbitrary poses. To address this challenge, we propose the Rotation-Equivariant Anchor Transformer (REVNET), a novel framework built upon the Vector Neuron (VN) network for robust point cloud completion under arbitrary rotations. To preserve local details, we represent partial point clouds as sets of equivariant anchors and design a VN Missing Anchor Transformer to predict the positions and features of missing anchors. Furthermore, we extend VN networks with a rotation-equivariant bias formulation and a ZCA-based layer normalization to improve feature expressiveness. Leveraging the flexible conversion between equivariant and invariant VN features, our model can generate point coordinates with greater stability. Experimental results show that our method outperforms state-of-the-art approaches on the synthetic MVP dataset in the equivariant setting. On the real-world KITTI dataset, REVNET delivers competitive results compared to non-equivariant networks, without requiring input pose alignment. The source code will be released on GitHub under URL: https://github.com/nizhf/REVNET.