# Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D

arXiv: https://arxiv.org/abs/2401.12046 · HTML: https://mlsanity.com/paper/2401.12046/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 52 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 30 of 43)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [RVT: Robotic View Transformer for 3D Object Manipulation](https://mlsanity.com/paper/2306.14896/) (2023)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Robotic Pick-and-Place of Novel Objects in Clutter with Multi-Affordance Grasping and Cross-Domain Image Matching](https://mlsanity.com/paper/1710.01330/) (2017)
- [Coarse-to-Fine Q-attention: Efficient Learning for Visual Robotic Manipulation via Discretisation](https://mlsanity.com/paper/2106.12534/) (2021)
- [Closing the Loop for Robotic Grasping: A Real-time, Generative Grasp Synthesis Approach](https://mlsanity.com/paper/1804.05172/) (2018)
- [Self-supervised 6D Object Pose Estimation for Robot Manipulation](https://mlsanity.com/paper/1909.10159/) (2019)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking](https://mlsanity.com/paper/2111.07786/) (2021)
- [You Only Demonstrate Once: Category-Level Manipulation from Single Visual Demonstration](https://mlsanity.com/paper/2201.12716/) (2022)
- [Learning to Rearrange Deformable Cables, Fabrics, and Bags with Goal-Conditioned Transporter Networks](https://mlsanity.com/paper/2012.03385/) (2020)
- [Multi-view Self-supervised Deep Learning for 6D Pose Estimation in the Amazon Picking Challenge](https://mlsanity.com/paper/1609.09475/) (2016)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (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)
- [Sample Efficient Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2202.09468/) (2022)

## Built on by (most cited first, 30 of 33)

- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [RVT-2: Learning Precise Manipulation from Few Demonstrations](https://mlsanity.com/paper/2406.08545/) (2024)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [FP3: A 3D Foundation Policy for Robotic Manipulation](https://mlsanity.com/paper/2503.08950/) (2025)
- [ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matching](https://mlsanity.com/paper/2409.04576/) (2024)
- [Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policies](https://mlsanity.com/paper/2406.11740/) (2024)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects](https://mlsanity.com/paper/2502.07005/) (2025)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space](https://mlsanity.com/paper/2507.01723/) (2025)
- [MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policies](https://mlsanity.com/paper/2409.15517/) (2024)
- [Constraint-Preserving Data Generation for Visuomotor Policy Learning](https://mlsanity.com/paper/2508.03944/) (2025)
- [Equivariant Offline Reinforcement Learning](https://mlsanity.com/paper/2406.13961/) (2024)
- [A Practical Guide for Incorporating Symmetry in Diffusion Policy](https://mlsanity.com/paper/2505.13431/) (2025)
- [3D Equivariant Visuomotor Policy Learning via Spherical Projection](https://mlsanity.com/paper/2505.16969/) (2025)
- [Equivariant Action Sampling for Reinforcement Learning and Planning](https://mlsanity.com/paper/2412.12237/) (2024)
- [EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AI](https://mlsanity.com/paper/2512.02020/) (2025)
- [On Universality of Deep Equivariant Networks](https://mlsanity.com/paper/2510.15814/) (2025)
- [Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environments](https://mlsanity.com/paper/2512.00915/) (2025)
- [Coarse-to-Fine 3D Keyframe Transporter](https://mlsanity.com/paper/2502.01773/) (2025)
- [Generalizable Hierarchical Skill Learning via Object-Centric Representation](https://mlsanity.com/paper/2510.21121/) (2025)
- [BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registration](https://mlsanity.com/paper/2407.08729/) (2024)
- [Precise Pick-and-Place using Score-Based Diffusion Networks](https://mlsanity.com/paper/2409.09725/) (2024)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [DidSee: Diffusion-Based Depth Completion for Material-Agnostic Robotic Perception and Manipulation](https://mlsanity.com/paper/2506.21034/) (2025)
- [Multi-Group Equivariant Augmentation for Reinforcement Learning in Robot Manipulation](https://mlsanity.com/paper/2508.11204/) (2025)
- [Group-Invariant Unsupervised Skill Discovery: Symmetry-aware Skill Representations for Generalizable Behavior](https://mlsanity.com/paper/2601.14000/) (2026)
- [Differential Amplifier-Inspired AmpAttention for Multi-View Robotic Manipulation](https://mlsanity.com/paper/2607.02845/) (2026)
- [Action Map Policy: Learning 3D Closed-loop Manipulation via Pixel Classification](https://mlsanity.com/paper/2607.10706/) (2026)

## Abstract (arXiv)

Many complex robotic manipulation tasks can be decomposed as a sequence of pick and place actions. Training a robotic agent to learn this sequence over many different starting conditions typically requires many iterations or demonstrations, especially in 3D environments. In this work, we propose Fourier Transporter (FourTran) which leverages the two-fold SE(d)xSE(d) symmetry in the pick-place problem to achieve much higher sample efficiency. FourTran is an open-loop behavior cloning method trained using expert demonstrations to predict pick-place actions on new environments. FourTran is constrained to incorporate symmetries of the pick and place actions independently. Our method utilizes a fiber space Fourier transformation that allows for memory-efficient construction. We test our proposed network on the RLbench benchmark and achieve state-of-the-art results across various tasks.