# EquAct: An SE(3)-Equivariant Multi-Task Transformer for Open-Loop Robotic Manipulation

arXiv: https://arxiv.org/abs/2505.21351 · HTML: https://mlsanity.com/paper/2505.21351/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2025.

## Built on by (most cited first, 9 of 9)

- [Do You Know Where Your Camera Is? View-Invariant Policy Learning with Camera Conditioning](https://mlsanity.com/paper/2510.02268/) (2025)
- [SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space](https://mlsanity.com/paper/2507.01723/) (2025)
- [Robotic Manipulation via Imitation Learning: Taxonomy, Evolution, Benchmark, and Challenges](https://mlsanity.com/paper/2508.17449/) (2025)
- [Generalizable Hierarchical Skill Learning via Object-Centric Representation](https://mlsanity.com/paper/2510.21121/) (2025)
- [Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization](https://mlsanity.com/paper/2511.15194/) (2025)
- [EquiVLA: A General Framework for Rotationally Equivariant Vision-Language-Action Models](https://mlsanity.com/paper/2606.19784/) (2026)
- [Multi-Task Reinforcement Learning of Drone Aerobatics by Exploiting Geometric Symmetries](https://mlsanity.com/paper/2602.10997/) (2026)
- [RayViT: Ray-Conditioned Visual Representations for Viewpoint-Robust Imitation Learning](https://mlsanity.com/paper/2607.29622/) (2026)
- [Screw Attention: Rigid-Body Algebra Inside a Transformer](https://mlsanity.com/paper/2610.00904/) (2026)

## Abstract (arXiv)

Transformer architectures can effectively learn language-conditioned, multi-task 3D open-loop manipulation policies from demonstrations by jointly processing natural language instructions and 3D observations. However, although both the robot policy and language instructions inherently encode rich 3D geometric structures, standard transformers lack built-in guarantees of geometric consistency, often resulting in unpredictable behavior under SE(3) transformations of the scene. In this paper, we leverage SE(3) equivariance as a key structural property shared by both policy and language, and propose EquAct-a novel SE(3)-equivariant multi-task transformer. EquAct is theoretically guaranteed to be SE(3) equivariant and consists of two key components: (1) an efficient SE(3)-equivariant point cloud-based U-net with spherical Fourier features for policy reasoning, and (2) SE(3)-invariant Feature-wise Linear Modulation (iFiLM) layers for language conditioning. To evaluate its spatial generalization ability, we benchmark EquAct on 18 RLBench simulation tasks with both SE(3) and SE(2) scene perturbations, and on 4 physical tasks. EquAct performs state-of-the-art across these simulation and physical tasks.