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Relaxed Rotational Equivariance via G-Biases in Vision
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Proposes RREConv, a group-equivariant convolution with learnable G-Biases added to each group-transformed filter, relaxing strict rotational equivariance to handle rotational symmetry-breaking in classification and 2D detection.
Problem
Group equivariant convolutions (GConv) enforce strict rotational equivariance, but real-world image data often breaks rotational symmetry (RSB), so strict constraints fit poorly.
Approach
Add a set of learnable, zero-initialized G-Biases to each of the n group-transformed copies of a GConv filter, so filter copies are no longer identical and equivariance becomes approximate (relaxed), with the bias magnitude determining the relaxation level and learned end-to-end from data.
Key results
- On CIFAR-100 with C4, RRE improves top-1 accuracy over SRE by +0.8 (80.1 to 80.9 for RRENet-n-scale ablation), with only about 0.04M extra parameters.
- On PASCAL VOC07+12 with C4, RREDet-n reaches AP50 84.1 and AP50:95 65.2, comparable to YOLOv8-m (83.7/65.3) with about 11% of its parameters.
- On MS COCO2017, RREDet-n (C4) reports AP50:95 of 40.2, above YOLOv10-n (38.5), though its AP50 (55.2) is below YOLOv5-s (56.8).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add G-Biases to SRE (C2) (ablation) | RRENet · CIFAR-10 | Top-1 accuracy: 94.4 -> 95.0 (+0.6) | Helped |
| Add G-Biases to SRE (C2) (ablation) | RRENet · CIFAR-100 | Top-1 accuracy: 76.1 -> 76.6 (+0.5) | Helped |
| Add G-Biases to SRE (C2) (ablation) | RREDet · PASCAL VOC07+12 | AP50: 78.9 -> 80.1 (+1.2) | Helped |
| Add G-Biases to SRE (C2) (ablation) | RREDet · PASCAL VOC07+12 | AP50:95: 58.3 -> 59.7 (+1.4) | Helped |
| Add G-Biases to SRE (C4) (ablation) | RRENet · CIFAR-10 | Top-1 accuracy: 95.6 -> 96.5 (+0.9) | Helped |
| Add G-Biases to SRE (C4) (ablation) | RRENet · CIFAR-100 | Top-1 accuracy: 80.1 -> 80.9 (+0.8) | Helped |
| Add G-Biases to SRE (C4) (ablation) | RREDet · PASCAL VOC07+12 | AP50: 83.1 -> 84.1 (+1.0) | Helped |
| Add G-Biases to SRE (C4) (ablation) | RREDet · PASCAL VOC07+12 | AP50:95: 64.1 -> 65.2 (+1.1) | Helped |
| Add G-Biases to SRE (C6) (ablation) | RRENet · CIFAR-10 | Top-1 accuracy: 96.0 -> 96.8 (+0.8) | Helped |
| Add G-Biases to SRE (C6) (ablation) | RRENet · CIFAR-100 | Top-1 accuracy: 80.6 -> 81.3 (+0.7) | Helped |
| Add G-Biases to SRE (C6) (ablation) | RREDet · PASCAL VOC07+12 | AP50: 83.8 -> 84.5 (+0.7) | Helped |
| Add G-Biases to SRE (C6) (ablation) | RREDet · PASCAL VOC07+12 | AP50:95: 64.7 -> 65.5 (+0.8) | Helped |
Surprising findings
- On C2, the RRE and SRE models have lower CIFAR accuracy than the non-rotational NRE baseline, although they use about half the parameters.
Limitations
- Evaluation limited to discrete cyclic groups C_n and natural image datasets; 3D and other groups unexplored.
- Theoretical relaxation bound is only derived as a bias-dependent term; epsilon is not quantified in practice.
- Gains on CIFAR and VOC are modest (about 0.5 to 1.4 points).
Experimental setup
Datasets: CIFAR-10 CIFAR-100 PASCAL VOC07+12 MS COCO2017
Benchmarks: CIFAR-10 CIFAR-100 PASCAL VOC07+12 MS COCO2017
Metrics: Top-1 accuracy AP50 AP50:95 parameter count
Baselines: GConv (SRE) on C2/C4/C6/C8 NRE plain CNN WideResNet ResNeXt-29 DenseNet-BC Res2NeXt-29 YOLOv8-n/s/m YOLOv5-s YOLOv6-n YOLOv7-tiny YOLOv9-n YOLOv10-n
Builds on: group equivariant convolutional networks (G-CNN) ResNet YOLOv8 Ultralytics
Closest papers by meaning
- R2Det: Exploring Relaxed Rotation Equivariance in 2D Object Detection (ICLR 2025 · similarity 0.94)
- Probing Equivariance and Symmetry Breaking in Convolutional Networks (NeurIPS 2025 · similarity 0.88)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.88)
- On the Fourier analysis in the SO(3) space : the EquiLoPO Network (ICLR 2025 · similarity 0.86)
- Continuous Rotation Group Equivariant Network Inspired by Neural Population Coding (AAAI 2024 · similarity 0.85)
- A Regularization-Guided Equivariant Approach for Image Restoration (CVPR 2025 · similarity 0.85)
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