# Screw Attention: Rigid-Body Algebra Inside a Transformer

arXiv: https://arxiv.org/abs/2610.00904 · HTML: https://mlsanity.com/paper/2610.00904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [UniVLA: Learning to Act Anywhere with Task-centric Latent Actions](https://mlsanity.com/paper/2505.06111/) (2025)
- [LIBERO-Plus: In-depth Robustness Analysis of Vision-Language-Action Models](https://mlsanity.com/paper/2510.13626/) (2025)
- [Residual Reinforcement Learning for Robot Control](https://mlsanity.com/paper/1812.03201/) (2018)
- [LIBERO-PRO: Towards Robust and Fair Evaluation of Vision-Language-Action Models Beyond Memorization](https://mlsanity.com/paper/2510.03827/) (2025)
- [Residual Policy Learning](https://mlsanity.com/paper/1812.06298/) (2018)
- [MetaMorph: Learning Universal Controllers with Transformers](https://mlsanity.com/paper/2203.11931/) (2022)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [Body Transformer: Leveraging Robot Embodiment for Policy Learning](https://mlsanity.com/paper/2408.06316/) (2024)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [EquAct: An SE(3)-Equivariant Multi-Task Transformer for Open-Loop Robotic Manipulation](https://mlsanity.com/paper/2505.21351/) (2025)
- [Understanding URDF: A Dataset and Analysis](https://mlsanity.com/paper/2308.00514/) (2023)
- [Toward Embodiment Equivariant Vision-Language-Action Policy](https://mlsanity.com/paper/2509.14630/) (2025)
- [XMoP: Whole-Body Control Policy for Zero-shot Cross-Embodiment Neural Motion Planning](https://mlsanity.com/paper/2409.15585/) (2024)
- [Embedding Morphology into Transformers for Cross-Robot Policy Learning](https://mlsanity.com/paper/2603.00182/) (2026)
- [Physics-Informed Policy Optimization via Analytic Dynamics Regularization](https://mlsanity.com/paper/2603.14469/) (2026)
- [MINERVA: How Small Can a Manipulation Policy Be and Still Solve LIBERO?](https://mlsanity.com/paper/2609.03715/) (2026)
- [MUKCa: Accurate and Affordable Cobot Calibration Without External Measurement Devices](https://mlsanity.com/paper/2503.12584/) (2025)
- [Rodrigues Network for Learning Robot Actions](https://mlsanity.com/paper/2506.02618/) (2025)
- [Articulated-Body Dynamics Network: Dynamics-Grounded Prior for Robot Learning](https://mlsanity.com/paper/2603.19078/) (2026)
- [KING: Embodiment-Aware Kinematic Graph Neural Network for Unified Motion Representation of Legged and Wheeled Robots](https://mlsanity.com/paper/2608.01015/) (2026)
- [SAVLA: Symmetry-Aware Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2609.16641/) (2026)

## Abstract (arXiv)

Learned manipulation policies rediscover from data the spatial relations that rigid-body mechanics supplies in closed form, which leaves them fragile to geometric change. We present Screw Attention, a transformer layer in which the relation between two bodies is a spatial transform rather than a graph edge. Each pair of tokens carries the relative pose and, for robot joints, the joint screw. Messages are transported along this relation into the receiver's frame, while the attention scores see only frame-invariant quantities. By construction, the messages are equivariant to an independent change of frame at every token, and a single layer can express the velocity recursion of rigid-body mechanics. On LIBERO-Spatial, a policy of 16k parameters trained from object poses alone reaches 97.3% success, above graph, transformer and flat networks of the same size and a flat network with 27 times more parameters. Ablations show that the gain comes from transporting the correct relations, and that the structure pays most where the task requires relations between frames that nothing else supplies. The equivariance makes the policy robust to how the robot is described, where every other learned network collapses under a change of frame convention. Furthermore, the policy tolerates pose noise and calibration errors at least as well as an analytic controller. Used as a gated residual on an analytic controller, it also improves a contact-rich insertion task. Code and trained policies will be released.