# R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection

arXiv: https://arxiv.org/abs/2408.11760 · HTML: https://mlsanity.com/paper/2408.11760/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 42 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [Object Detection in 20 Years: A Survey](https://mlsanity.com/paper/1905.05055/) (2019)
- [YOLOv10: Real-Time End-to-End Object Detection](https://mlsanity.com/paper/2405.14458/) (2024)
- [Res2Net: A New Multi-scale Backbone Architecture](https://mlsanity.com/paper/1904.01169/) (2019)
- [YOLOv9: Learning What You Want to Learn Using Programmable Gradient Information](https://mlsanity.com/paper/2402.13616/) (2024)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [A Comprehensive Review of YOLO Architectures in Computer Vision: From YOLOv1 to YOLOv8 and YOLO-NAS](https://mlsanity.com/paper/2304.00501/) (2023)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks](https://mlsanity.com/paper/2007.02005/) (2020)
- [Revisiting Spatial Invariance with Low-Rank Local Connectivity](https://mlsanity.com/paper/2002.02959/) (2020)
- [Symmetry Breaking and Equivariant Neural Networks](https://mlsanity.com/paper/2312.09016/) (2023)
- [Deep Rotation Equivariant Network](https://mlsanity.com/paper/1705.08623/) (2017)
- [Approximately Equivariant Graph Networks](https://mlsanity.com/paper/2308.10436/) (2023)

## Built on by (most cited first, 4 of 4)

- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [Tunable Soft Equivariance with Guarantees](https://mlsanity.com/paper/2603.26657/) (2026)
- [Factorized Neural Operators Decompose Dynamic and Persistent Responses](https://mlsanity.com/paper/2606.16900/) (2026)
- [Geometric Causal Models](https://mlsanity.com/paper/2607.05153/) (2026)

## Abstract (arXiv)

Group Equivariant Convolution (GConv) empowers models to explore underlying symmetry in data, improving performance. However, real-world scenarios often deviate from ideal symmetric systems caused by physical permutation, characterized by non-trivial actions of a symmetry group, resulting in asymmetries that affect the outputs, a phenomenon known as Symmetry Breaking. Traditional GConv-based methods are constrained by rigid operational rules within group space, assuming data remains strictly symmetry after limited group transformations. This limitation makes it difficult to adapt to Symmetry-Breaking and non-rigid transformations. Motivated by this, we mainly focus on a common scenario: Rotational Symmetry-Breaking. By relaxing strict group transformations within Strict Rotation-Equivariant group Cn, we redefine a Relaxed Rotation-Equivariant group Rn and introduce a novel Relaxed Rotation-Equivariant GConv (R2GConv) with only a minimal increase of 4n parameters compared to GConv. Based on R2GConv, we propose a Relaxed Rotation-Equivariant Network (R2Net) as the backbone and develop a Relaxed Rotation-Equivariant Object Detector (R2Det) for 2D object detection. Experimental results demonstrate the effectiveness of the proposed R2GConv in natural image classification, and R2Det achieves excellent performance in 2D object detection with improved generalization capabilities and robustness. The code is available in texttthttps://github.com/wuer5/r2det.