# Equivariant Point Cloud Analysis via Learning Orientations for Message Passing

arXiv: https://arxiv.org/abs/2203.14486 · HTML: https://mlsanity.com/paper/2203.14486/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [Category-Level Articulated Object Pose Estimation](https://mlsanity.com/paper/1912.11913/) (2019)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [Unsupervised Geometry-Aware Representation for 3D Human Pose Estimation](https://mlsanity.com/paper/1804.01110/) (2018)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Canonical Capsules: Self-Supervised Capsules in Canonical Pose](https://mlsanity.com/paper/2012.04718/) (2020)
- [Global Context Aware Convolutions for 3D Point Cloud Understanding](https://mlsanity.com/paper/2008.02986/) (2020)

## Built on by (most cited first, 30 of 32)

- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [Equivariant Frames and the Impossibility of Continuous Canonicalization](https://mlsanity.com/paper/2402.16077/) (2024)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [Graph Neural Network with Local Frame for Molecular Potential Energy Surface](https://mlsanity.com/paper/2208.00716/) (2022)
- [Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariance](https://mlsanity.com/paper/2304.10528/) (2023)
- [NeuralBF: Neural Bilateral Filtering for Top-down Instance Segmentation on Point Clouds](https://mlsanity.com/paper/2207.09978/) (2022)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [Latent Field Discovery In Interacting Dynamical Systems With Neural Fields](https://mlsanity.com/paper/2310.20679/) (2023)
- [Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis](https://mlsanity.com/paper/2403.11113/) (2024)
- [Rethinking Rotation Invariance with Point Cloud Registration](https://mlsanity.com/paper/2301.00149/) (2022)
- [Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning](https://mlsanity.com/paper/2502.02247/) (2025)
- [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)
- [Geometric Point Attention Transformer for 3D Shape Reassembly](https://mlsanity.com/paper/2411.17788/) (2024)
- [Combinative Matching for Geometric Shape Assembly](https://mlsanity.com/paper/2508.09780/) (2025)
- [Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks](https://mlsanity.com/paper/2509.24886/) (2025)
- [TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis](https://mlsanity.com/paper/2211.14456/) (2022)
- [Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillation](https://mlsanity.com/paper/2308.04725/) (2023)
- [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024)
- [Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environments](https://mlsanity.com/paper/2407.12505/) (2024)
- [Towards a 3D Transfer-based Black-box Attack via Critical Feature Guidance](https://mlsanity.com/paper/2508.15650/) (2025)
- [Frame-based Equivariant Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2509.19506/) (2025)
- [Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbits](https://mlsanity.com/paper/2305.19889/) (2023)
- [Point-PNG: Conditional Pseudo-Negatives Generation for Point Cloud Pre-Training](https://mlsanity.com/paper/2409.15832/) (2024)
- [HFBRI-MAE: Handcrafted Feature Based Rotation-Invariant Masked Autoencoder for 3D Point Cloud Analysis](https://mlsanity.com/paper/2504.14132/) (2025)
- [Stable and Accurate Orbital-Free DFT Powered by Machine Learning](https://mlsanity.com/paper/2503.00443/) (2025)

## Abstract (arXiv)

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decouple the relative position for each point from the global pose of the entire point cloud. Therefore, we extend current message passing networks with a module that learns orientations for each point. Before aggregating information from the neighbors of a point, the networks transforms the neighbors' coordinates based on the point's learned orientations. We provide formal proofs to show the equivariance of the proposed framework. Empirically, we demonstrate that our proposed method is competitive on both point cloud analysis and physical modeling tasks. Code is available at https://github.com/luost26/Equivariant-OrientedMP .