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R2Det: Exploring Relaxed Rotation Equivariance in 2D Object Detection
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Proposes R2Det, a relaxed rotation-equivariant object detector built from learnable perturbations of the C_n rotation group (R2GConv, R2Net backbone), reporting gains over SRE and YOLOv8 on VOC and COCO with fewer parameters.
Problem
Strict rotation-equivariant convolutions assume perfect symmetry, which breaks on real images with rotational symmetry-breaking, limiting 2D object detection performance and robustness.
Approach
Relax the strict cyclic group C_n by adding a learnable perturbation matrix Delta (4 params per rotation) to each affine rotation matrix, forming a relaxed group R_n; filters are built by resampling a Kaiming-initialized weight through these perturbed transforms, yielding R2GConv with only 4n extra parameters per layer.
Key results
- On COCO val, R2Det-N (C4) reaches 43.7 AP50:95 vs 37.3 for YOLOv8-N with 2.8M vs 3.2M params.
- Replacing SRE with RRE in R2Det-N (C4) improves VOC AP50:95 from 64.2 to 65.1 at a cost of only 512 extra parameters.
- R2Det-M (C4) reaches 87.3 AP50 on VOC, above YOLOv8-X's 86.9, with 22.6M params versus 68.1M.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace strict rotation-equivariant filters with relaxed rotation-equivariant filters (ablation) | R2Det-N · VOC test, C4 | AP50:95: 64.2 -> 65.1 (+0.9) | Helped |
| replace strict rotation-equivariant filters with relaxed rotation-equivariant filters (ablation) | R2Det-N · COCO val, C4 | AP50:95: 43.2 -> 43.7 (+0.5) | Helped |
| replace strict filters with relaxed filters (ablation) | R2Det-N · VOC test, C2/C4/C8 | AP50:95: +0.6 / +0.9 / +1.5 | Helped |
| replace strict filters with relaxed filters (ablation) | R2Det-N · COCO val, C2/C4/C8 | AP50:95: +0.4 / +0.5 / +0.7 | Helped |
| initialize perturbations with b=0.1 rather than b=0 (ablation) | R2Det-N (C4) · VOC test | AP50: 83.8 -> 84.1 | Helped |
| increase perturbation initialization boundary from b=0.1 to b=0.2 (ablation) | R2Det-N (C4) · VOC test | AP50: 84.1 -> 83.5 | Hurt |
| increase perturbation initialization boundary from b=0.1 to b=0.4 (ablation) | R2Det-N (C4) · VOC test | AP50: 84.1 -> 83.6 | Hurt |
| increase perturbation initialization boundary from b=0.1 to b=0.6 (ablation) | R2Det-N (C4) · VOC test | AP50: 84.1 -> 82.4 | Hurt |
| increase perturbation initialization boundary from b=0.1 to b=0.8 (ablation) | R2Det-N (C4) · VOC test | AP50: 84.1 -> 80.7 | Hurt |
| add learnable noise to standard convolution filters (ablation) | YOLOv8-N · VOC test | AP50: 78.6 -> 73.1 (-5.5) | Hurt |
| replace standard convolutions with strict rotation-equivariant filters (ablation) | YOLOv8-N · VOC test, C4 | AP50:95: 57.5 -> 62.8 | Helped |
| replace strict rotation-equivariant filters with relaxed filters (ablation) | YOLOv8-N · VOC test, C4 | AP50:95: 62.8 -> 64.2 (+1.4) | Helped |
Surprising findings
- Adding the same learnable noise to standard YOLOv8 convolutions degrades performance (AP50:95 57.5 to 51.4), so the gain depends on the group structure.
- Setting the perturbation initialization to zero still yields a different model from strict SRE because the perturbation is learned end-to-end.
Limitations
- Relaxation is restricted to the rotation group C_n; other symmetries and transformations are not explored.
- Gains over SRE are modest (roughly 0.5 to 1.5 AP points) and results come from single runs in the reported tables.
- Some ablations are only on small models (N variant) and the rotated-MNIST robustness test is self-constructed.
Experimental setup
Datasets: PASCAL VOC07+12 MS COCO 2017 CIFAR-10 CIFAR-100 COCO-seg MNIST ROT-MNIST (self-constructed)
Benchmarks: PASCAL VOC test COCO val2017 CIFAR-10 CIFAR-100 COCO-seg
Metrics: AP50:95 AP50 AP75 AP_S/M/L Top-1 accuracy Params FLOPs Mask AP
Baselines: YOLOv8 YOLOv9 YOLOv10 SRE GConv (C_n) WideResNet ResNeXt-29 DenseNet-BC RTMDet-Ins YOLOv5 YOLOv7
Builds on: G-CNN YOLOv8 Res2Net approximate equivariance
Closest papers by meaning
- Relaxed Rotational Equivariance via G-Biases in Vision (AAAI 2025 · similarity 0.94)
- Probing Equivariance and Symmetry Breaking in Convolutional Networks (NeurIPS 2025 · similarity 0.88)
- FRED: Towards a Full Rotation-Equivariance in Aerial Image Object Detection (AAAI 2024 · similarity 0.88)
- ReDiffDet: Rotation-equivariant Diffusion Model for Oriented Object Detection (CVPR 2025 · similarity 0.87)
- Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection (CVPR 2025 · similarity 0.87)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.86)
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