# Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds

arXiv: https://arxiv.org/abs/2308.06271 · HTML: https://mlsanity.com/paper/2308.06271/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 27 Jul 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Learning with invariances in random features and kernel models](https://mlsanity.com/paper/2102.13219/) (2021)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [Endowing Deep 3D Models with Rotation Invariance Based on Principal Component Analysis](https://mlsanity.com/paper/1910.08901/) (2019)
- [Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks)](https://mlsanity.com/paper/1803.10743/) (2018)
- [Sketching Algorithms and Lower Bounds for Ridge Regression](https://mlsanity.com/paper/2204.06653/) (2022)

## Built on by (most cited first, 2 of 2)

- [RAPiD-Seg: Range-Aware Pointwise Distance Distribution Networks for 3D LiDAR Segmentation](https://mlsanity.com/paper/2407.10159/) (2024)
- [TraIL-Det: Transformation-Invariant Local Feature Networks for 3D LiDAR Object Detection with Unsupervised Pre-Training](https://mlsanity.com/paper/2408.13902/) (2024)

## Abstract (arXiv)

Rotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many tasks, including molecular property prediction and 3D shape classification. These methods generally either rely on task-specific rotation-invariant features, or they use general-purpose deep neural networks which are complicated to design and train. However, it is unclear whether the success of these methods is primarily due to the rotation invariance or the deep neural networks. To address this question, we suggest a simple and general-purpose method for learning rotation-invariant functions of three-dimensional point cloud data using a random features approach. Specifically, we extend the random features method of Rahimi & Recht 2007 by deriving a version that is invariant to three-dimensional rotations and showing that it is fast to evaluate on point cloud data. We show through experiments that our method matches or outperforms the performance of general-purpose rotation-invariant neural networks on standard molecular property prediction benchmark datasets QM7 and QM9. We also show that our method is general-purpose and provides a rotation-invariant baseline on the ModelNet40 shape classification task. Finally, we show that our method has an order of magnitude smaller prediction latency than competing kernel methods.