# EqvAfford: SE(3) Equivariance for Point-Level Affordance Learning

arXiv: https://arxiv.org/abs/2408.01953 · HTML: https://mlsanity.com/paper/2408.01953/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 41 references that are in the map.
- First posted on arXiv 4 Aug 2024.

## Builds on (most cited first, 30 of 35)

- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Where2Act: From Pixels to Actions for Articulated 3D Objects](https://mlsanity.com/paper/2101.02692/) (2021)
- [ContactDB: Analyzing and Predicting Grasp Contact via Thermal Imaging](https://mlsanity.com/paper/1904.06830/) (2019)
- [General Flow as Foundation Affordance for Scalable Robot Learning](https://mlsanity.com/paper/2401.11439/) (2024)
- [VAT-Mart: Learning Visual Action Trajectory Proposals for Manipulating 3D ARTiculated Objects](https://mlsanity.com/paper/2106.14440/) (2021)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Robo-ABC: Affordance Generalization Beyond Categories via Semantic Correspondence for Robot Manipulation](https://mlsanity.com/paper/2401.07487/) (2024)
- [ScrewNet: Category-Independent Articulation Model Estimation From Depth Images Using Screw Theory](https://mlsanity.com/paper/2008.10518/) (2020)
- [RAM: Retrieval-Based Affordance Transfer for Generalizable Zero-Shot Robotic Manipulation](https://mlsanity.com/paper/2407.04689/) (2024)
- [AdaAfford: Learning to Adapt Manipulation Affordance for 3D Articulated Objects via Few-shot Interactions](https://mlsanity.com/paper/2112.00246/) (2021)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fields](https://mlsanity.com/paper/2211.09786/) (2022)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Edge Grasp Network: A Graph-Based SE(3)-invariant Approach to Grasp Detection](https://mlsanity.com/paper/2211.00191/) (2022)
- [Where2Explore: Few-shot Affordance Learning for Unseen Novel Categories of Articulated Objects](https://mlsanity.com/paper/2309.07473/) (2023)
- [DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly](https://mlsanity.com/paper/2402.19302/) (2024)
- [Neural Grasp Distance Fields for Robot Manipulation](https://mlsanity.com/paper/2211.02647/) (2022)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulation](https://mlsanity.com/paper/2209.13864/) (2022)
- [Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation](https://mlsanity.com/paper/2303.11057/) (2023)
- [Learning Environment-Aware Affordance for 3D Articulated Object Manipulation under Occlusions](https://mlsanity.com/paper/2309.07510/) (2023)
- [UniGarmentManip: A Unified Framework for Category-Level Garment Manipulation via Dense Visual Correspondence](https://mlsanity.com/paper/2405.06903/) (2024)
- [DualAfford: Learning Collaborative Visual Affordance for Dual-gripper Manipulation](https://mlsanity.com/paper/2207.01971/) (2022)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [UniDoorManip: Learning Universal Door Manipulation Policy Over Large-scale and Diverse Door Manipulation Environments](https://mlsanity.com/paper/2403.02604/) (2024)
- [Articulated Object Manipulation with Coarse-to-fine Affordance for Mitigating the Effect of Point Cloud Noise](https://mlsanity.com/paper/2402.18699/) (2024)

## Built on by (most cited first, 6 of 6)

- [ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policy](https://mlsanity.com/paper/2411.03990/) (2024)
- [AffordanceVLA: A Vision-Language-Action Model Empowering Action Generation through Affordance-Aware Understanding](https://mlsanity.com/paper/2606.06155/) (2026)
- [Learning Part-Aware Dense 3D Feature Field for Generalizable Articulated Object Manipulation](https://mlsanity.com/paper/2602.14193/) (2026)
- [Diffusion Model as a Generalist Segmentation Learner](https://mlsanity.com/paper/2604.24575/) (2026)
- [SUGAR: A Scalable Human-Video-Driven Generalizable Humanoid Loco-Manipulation Learning Framework](https://mlsanity.com/paper/2605.20373/) (2026)
- [Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization](https://mlsanity.com/paper/2511.15194/) (2025)

## Abstract (arXiv)

Humans perceive and interact with the world with the awareness of equivariance, facilitating us in manipulating different objects in diverse poses. For robotic manipulation, such equivariance also exists in many scenarios. For example, no matter what the pose of a drawer is (translation, rotation and tilt), the manipulation strategy is consistent (grasp the handle and pull in a line). While traditional models usually do not have the awareness of equivariance for robotic manipulation, which might result in more data for training and poor performance in novel object poses, we propose our EqvAfford framework, with novel designs to guarantee the equivariance in point-level affordance learning for downstream robotic manipulation, with great performance and generalization ability on representative tasks on objects in diverse poses.