# Design equivariant neural networks for 3D point cloud

arXiv: https://arxiv.org/abs/2205.00630 · HTML: https://mlsanity.com/paper/2205.00630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 26 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 23 of 23)

- [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)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [Universal Equivariant Multilayer Perceptrons](https://mlsanity.com/paper/2002.02912/) (2020)
- [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://mlsanity.com/paper/1803.01588/) (2018)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Equivalence of approximation by convolutional neural networks and fully-connected networks](https://mlsanity.com/paper/1809.00973/) (2018)
- [Rotation-Invariant Local-to-Global Representation Learning for 3D Point Cloud](https://mlsanity.com/paper/2010.03318/) (2020)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [Universal Approximation Theorem for Equivariant Maps by Group CNNs](https://mlsanity.com/paper/2012.13882/) (2020)
- [Quaternion Product Units for Deep Learning on 3D Rotation Groups](https://mlsanity.com/paper/1912.07791/) (2019)
- [Dynamic Steerable Blocks in Deep Residual Networks](https://mlsanity.com/paper/1706.00598/) (2017)

## Abstract (arXiv)

This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The main challenge when designing equivariant models for point clouds is how to trade-off the performance of the model and the complexity. Existing equivariant models are either too complicate to implement or very high complexity. The main aim of this study is to build a general procedure to introduce group equivariant property to SOTA models for 3D point clouds. The group equivariant models built form our procedure are simple to implement, less complexity in comparison with the existing ones, and they preserve the strengths of the original SOTA backbone. From the results of the experiments on object classification, it is shown that our methods are superior to other group equivariant models in performance and complexity. Moreover, our method also helps to improve the mIoU of semantic segmentation models. Overall, by using a combination of only-finite-rotation equivariance and augmentation, our models can outperform existing full SO(3)-equivariance models with much cheaper complexity and GPU memory. The proposed procedure is general and forms a fundamental approach to group equivariant neural networks. We believe that it can be easily adapted to other SOTA models in the future.