# Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization

arXiv: https://arxiv.org/abs/2511.15194 · HTML: https://mlsanity.com/paper/2511.15194/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [A Survey on Vision-Language-Action Models for Embodied AI](https://mlsanity.com/paper/2405.14093/) (2024)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [An Attention Enhanced Graph Convolutional LSTM Network for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1902.09130/) (2019)
- [A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms](https://mlsanity.com/paper/1907.03146/) (2019)
- [Large Language Models for Robotics: A Survey](https://mlsanity.com/paper/2311.07226/) (2023)
- [Diffusion Model is an Effective Planner and Data Synthesizer for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2305.18459/) (2023)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Diversify Your Vision Datasets with Automatic Diffusion-Based Augmentation](https://mlsanity.com/paper/2305.16289/) (2023)
- [ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policy](https://mlsanity.com/paper/2411.03990/) (2024)
- [Leveraging Symmetries in Pick and Place](https://mlsanity.com/paper/2308.07948/) (2023)
- [Learning Efficient and Robust Language-conditioned Manipulation using Textual-Visual Relevancy and Equivariant Language Mapping](https://mlsanity.com/paper/2406.15677/) (2024)
- [EquAct: An SE(3)-Equivariant Multi-Task Transformer for Open-Loop Robotic Manipulation](https://mlsanity.com/paper/2505.21351/) (2025)
- [EqvAfford: SE(3) Equivariance for Point-Level Affordance Learning](https://mlsanity.com/paper/2408.01953/) (2024)

## Built on by (most cited first, 2 of 2)

- [EquiVLA: A General Framework for Rotationally Equivariant Vision-Language-Action Models](https://mlsanity.com/paper/2606.19784/) (2026)
- [The Robot Is Not Its Description: GaugeBench for Representation Robustness in Morphology-Aware Policies](https://mlsanity.com/paper/2610.07597/) (2026)

## Abstract (arXiv)

Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations and translations. While recent works attempt to introduce equivariance through bespoke architectural modifications, these methods suffer from high implementation complexity, computational cost, and poor portability. Inspired by human cognitive processes in spatial reasoning, we propose Eq.Bot, a universal canonicalization framework grounded in SE(2) group equivariant theory for robotic manipulation learning. Our framework transforms observations into a canonical space, applies an existing policy, and maps the resulting actions back to the original space. As a model-agnostic solution, Eq.Bot aims to endow models with spatial equivariance without requiring architectural modifications. Extensive experiments demonstrate the superiority of Eq.Bot under both CNN-based (e.g., CLIPort) and Transformer-based (e.g., OpenVLA-OFT) architectures over existing methods on various robotic manipulation tasks, where the most significant improvement can reach 50.0%.