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Learning Color Equivariant Representations
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Introduces color-equivariant group CNNs (hue, saturation, luminance) using an input-image lifting layer that avoids the invalid RGB values of CEConv, yielding much lower equivariance error and better OOD color generalization.
Problem
Standard CNNs are sensitive to color variation (hue, saturation, luminance shifts), and prior hue-equivariant CEConv lifts via RGB filters that produce invalid RGB values, breaking equivariance and hurting performance.
Approach
Model hue as the cyclic group C_N, saturation and luminance as discrete translation groups in HSL space, and lift the input image directly by applying group actions to HSL pixel values (rather than to RGB filters), so that equivariance holds without projection artifacts; build group convolutions over the resulting product groups.
Key results
- Hue-4 lifting layer reduces equivariance error by more than three orders of magnitude relative to CEConv-4.
- On Hue-shift MNIST out-of-distribution (A/B), Hue-3* achieves 1.81% error versus 57.38% for Z2CNN.
- On Camelyon17 saturation shift, Sat-3* achieves 16.08% error versus 28.91% for ResNet50.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use hue-equivariant Hue-4 instead of Z2CNN | Z2CNN · Hue-shift MNIST A/B | classification error: 57.38 (22.06) -> 2.08 (0.15) | Helped |
| Use Hue-4 instead of Z2CNN | Z2CNN · Hue-shift MNIST A/A | classification error: 1.54 (0.10) -> 1.97 (0.25) | Mixed |
| Use hue-equivariant Hue-4 instead of Z2CNN | Z2CNN · Hue-shift 3D Shapes A/B | classification error: 51.25 (9.59) -> 0.00 (0.00) | Helped |
| Use hue-equivariant Hue-4 instead of Z2CNN | Z2CNN · Hue-shift 3D Shapes A/C | classification error: 26.66 (19.60) -> 0.00 (0.00) | Helped |
| Use saturation-equivariant Sat-3 instead of ResNet50 | ResNet50 · Camelyon17 | classification error: 28.91 (7.58) -> 16.08 (2.68) | Helped |
| Use Hue-4 instead of ResNet | ResNet · Caltech-101 | classification error: 32.68 (1.55) -> 32.23 (1.07) | Helped |
| Use Hue-4 instead of ResNet | ResNet · CIFAR-10 | classification error: 7.86 (1.14) -> 8.83 (0.64) | Hurt |
| Use Hue-4 instead of ResNet | ResNet · CIFAR-100 | classification error: 32.00 (0.63) -> 34.70 (0.89) | Hurt |
| Use Hue-4 instead of ResNet | ResNet · Stanford Cars | classification error: 25.41 (0.96) -> 20.38 (1.06) | Helped |
| Use Hue-4 instead of ResNet | ResNet · Oxford Pets | classification error: 31.52 (2.05) -> 27.39 (0.68) | Helped |
| Use Hue-4 instead of ResNet | ResNet · STL-10 | classification error: 18.59 (1.65) -> 20.73 (1.11) | Hurt |
| Transform input images in the lifting layer instead of rotating RGB filters | Hue-equivariant lifting layer · Hue-shift 3D Shapes | equivariance error: more than three orders of magnitude | Helped |
Surprising findings
- CEConv-4 suffers large generalization errors on 3D Shapes (0.60% and 0.53% OOD) compared with Hue-4 (0.00%), attributed to feature map equivariance error.
- Color-equivariant models did not improve in-distribution performance on CIFAR-10; hue-equivariant model was on-par with conventional CNN.
Limitations
- GCNNs are more computationally expensive than conventional CNNs due to filter orbit computation at each layer.
- Finite filter orbit only approximates a continuous group.
- Saturation and luminance groups are discretized and approximated via bijection to (Z,+).
Experimental setup
Datasets: MNIST 3D Shapes Camelyon17 Caltech-101 Oxford-IIT Pets Stanford Cars STL-10 CIFAR-10 CIFAR-100 small NORB Tiny-ImageNet
Benchmarks: Hue-shift MNIST Hue-shift 3D Shapes Camelyon17 Caltech-101 Oxford-IIT Pets Stanford Cars STL-10 CIFAR-10 CIFAR-100
Metrics: classification error relative equivariance error sample efficiency error improvement
Baselines: ResNet ResNet-aug ResNet-gray CEConv-3 CEConv-4 Z2CNN ResNet50
Builds on: Color Equivariant Convolutional Networks (CEConv) group equivariant convolutional networks (G-CNN) Z2CNN
Closest papers by meaning
- Color Equivariant Convolutional Networks (NeurIPS 2023 · similarity 0.92)
- A Hypertoroidal Covering for Perfect Color Equivariance (ICML 2026 · similarity 0.91)
- Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts (ICML 2024 · similarity 0.90)
- Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters (NeurIPS 2024 · similarity 0.86)
- Probing Equivariance and Symmetry Breaking in Convolutional Networks (NeurIPS 2025 · similarity 0.86)
- A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs (ICML 2024 · similarity 0.86)
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