# USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulation

arXiv: https://arxiv.org/abs/2209.13864 · HTML: https://mlsanity.com/paper/2209.13864/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 28 Sep 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [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)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [Dense Object Nets: Learning Dense Visual Object Descriptors By and For Robotic Manipulation](https://mlsanity.com/paper/1806.08756/) (2018)
- [Self-Supervised Correspondence in Visuomotor Policy Learning](https://mlsanity.com/paper/1909.06933/) (2019)
- [You Only Demonstrate Once: Category-Level Manipulation from Single Visual Demonstration](https://mlsanity.com/paper/2201.12716/) (2022)
- [Discovery of Latent 3D Keypoints via End-to-end Geometric Reasoning](https://mlsanity.com/paper/1807.03146/) (2018)
- [6-PACK: Category-level 6D Pose Tracker with Anchor-Based Keypoints](https://mlsanity.com/paper/1910.10750/) (2019)
- [USIP: Unsupervised Stable Interest Point Detection from 3D Point Clouds](https://mlsanity.com/paper/1904.00229/) (2019)
- [Keypoints into the Future: Self-Supervised Correspondence in Model-Based Reinforcement Learning](https://mlsanity.com/paper/2009.05085/) (2020)
- [KeypointNet: A Large-scale 3D Keypoint Dataset Aggregated from Numerous Human Annotations](https://mlsanity.com/paper/2002.12687/) (2020)
- [Learning Rope Manipulation Policies Using Dense Object Descriptors Trained on Synthetic Depth Data](https://mlsanity.com/paper/2003.01835/) (2020)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)
- [Unsupervised Learning of Visual 3D Keypoints for Control](https://mlsanity.com/paper/2106.07643/) (2021)
- [S3K: Self-Supervised Semantic Keypoints for Robotic Manipulation via Multi-View Consistency](https://mlsanity.com/paper/2009.14711/) (2020)
- [kPAM-SC: Generalizable Manipulation Planning using KeyPoint Affordance and Shape Completion](https://mlsanity.com/paper/1909.06980/) (2019)
- [Skeleton Merger: an Unsupervised Aligned Keypoint Detector](https://mlsanity.com/paper/2103.10814/) (2021)
- [Category-level 6D Object Pose Recovery in Depth Images](https://mlsanity.com/paper/1808.00255/) (2018)
- [Pointwise Rotation-Invariant Network with Adaptive Sampling and 3D Spherical Voxel Convolution](https://mlsanity.com/paper/1811.09361/) (2018)
- [UKPGAN: A General Self-Supervised Keypoint Detector](https://mlsanity.com/paper/2011.11974/) (2020)
- [PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features](https://mlsanity.com/paper/2102.12093/) (2021)
- [3D Interest Point Detection via Discriminative Learning](https://mlsanity.com/paper/1312.6826/) (2013)

## Built on by (most cited first, 27 of 27)

- [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)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policy](https://mlsanity.com/paper/2411.03990/) (2024)
- [ClothesNet: An Information-Rich 3D Garment Model Repository with Simulated Clothes Environment](https://mlsanity.com/paper/2308.09987/) (2023)
- [UniGarmentManip: A Unified Framework for Category-Level Garment Manipulation via Dense Visual Correspondence](https://mlsanity.com/paper/2405.06903/) (2024)
- [SparseDFF: Sparse-View Feature Distillation for One-Shot Dexterous Manipulation](https://mlsanity.com/paper/2310.16838/) (2023)
- [SKIL: Semantic Keypoint Imitation Learning for Generalizable Data-efficient Manipulation](https://mlsanity.com/paper/2501.14400/) (2025)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [Leveraging Symmetries in Pick and Place](https://mlsanity.com/paper/2308.07948/) (2023)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [A Survey of Robotic Navigation and Manipulation with Physics Simulators in the Era of Embodied AI](https://mlsanity.com/paper/2505.01458/) (2025)
- [Leveraging Locality to Boost Sample Efficiency in Robotic Manipulation](https://mlsanity.com/paper/2406.10615/) (2024)
- [Two by Two: Learning Multi-Task Pairwise Objects Assembly for Generalizable Robot Manipulation](https://mlsanity.com/paper/2504.06961/) (2025)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [ArrayBot: Reinforcement Learning for Generalizable Distributed Manipulation through Touch](https://mlsanity.com/paper/2306.16857/) (2023)
- [SC3K: Self-supervised and Coherent 3D Keypoints Estimation from Rotated, Noisy, and Decimated Point Cloud Data](https://mlsanity.com/paper/2308.05410/) (2023)
- [EqvAfford: SE(3) Equivariance for Point-Level Affordance Learning](https://mlsanity.com/paper/2408.01953/) (2024)
- [Key-Grid: Unsupervised 3D Keypoints Detection using Grid Heatmap Features](https://mlsanity.com/paper/2410.02237/) (2024)
- [Neural Attention Field: Emerging Point Relevance in 3D Scenes for One-Shot Dexterous Grasping](https://mlsanity.com/paper/2410.23039/) (2024)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [SelfGeo: Self-supervised and Geodesic-consistent Estimation of Keypoints on Deformable Shapes](https://mlsanity.com/paper/2408.02291/) (2024)
- [Interacted Planes Reveal 3D Line Mapping](https://mlsanity.com/paper/2602.01296/) (2026)
- [SimpleMatch: A Simple and Strong Baseline for Semantic Correspondence](https://mlsanity.com/paper/2601.12357/) (2026)
- [HeteroGenManip: Generalizable Manipulation For Heterogeneous Object Interactions](https://mlsanity.com/paper/2605.10201/) (2026)
- [KeyGen: Unsupervised Keypoint based Object-Centric Representations for Category-Level Policy Generalization](https://mlsanity.com/paper/2609.28818/) (2026)

## Abstract (arXiv)

Can a robot manipulate intra-category unseen objects in arbitrary poses with the help of a mere demonstration of grasping pose on a single object instance? In this paper, we try to address this intriguing challenge by using USEEK, an unsupervised SE(3)-equivariant keypoints method that enjoys alignment across instances in a category, to perform generalizable manipulation. USEEK follows a teacher-student structure to decouple the unsupervised keypoint discovery and SE(3)-equivariant keypoint detection. With USEEK in hand, the robot can infer the category-level task-relevant object frames in an efficient and explainable manner, enabling manipulation of any intra-category objects from and to any poses. Through extensive experiments, we demonstrate that the keypoints produced by USEEK possess rich semantics, thus successfully transferring the functional knowledge from the demonstration object to the novel ones. Compared with other object representations for manipulation, USEEK is more adaptive in the face of large intra-category shape variance, more robust with limited demonstrations, and more efficient at inference time.