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Normalize Filters! Classical Wisdom for Deep Vision
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Proposes filter normalization (normalizing positive and negative convolution weights separately, followed by learnable scale and shift) so CNN/ViT filters become atmosphere-equivariant and robust to gain-bias intensity changes.
Problem
Learned convolutional filters are unnormalized, so their responses shift and distort under affine intensity changes (gain/bias from atmospheric transfer, illumination, haze), degrading classification robustness.
Approach
Normalize the positive and negative weight parts of each convolution filter separately (L1 norm to 1 each), then apply learnable scaling and shifting akin to batch normalization, making filters either averaging or differencing and yielding gain/offset equivariance without data augmentation.
Key results
- On ImageNet, R34N averages 67.0% on corrupted sets versus 2.1% for R34 and about 14.3% for CLIP-B, while R34N has 22M parameters versus CLIP's 151M.
- On CIFAR-10 with R20, filter normalization raises the D_S accuracy from 38.1% to 89.5%, with the clean accuracy kept at about 91.5%.
- On ExDark zero-shot, R34N reaches 34.2% accuracy versus 28.3% for R34.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add filter normalization | ResNet20 · CIFAR-10 D_C | accuracy: 87.9 -> 91.1 | Helped |
| Add filter normalization | ResNet20 · CIFAR-10 D_L | accuracy: 84.2 -> 89.6 | Helped |
| Add filter normalization | ResNet20 · CIFAR-10 D_B | accuracy: 82.9 -> 85.5 | Helped |
| Add filter normalization | ResNet20 · CIFAR-10 D_S | accuracy: 38.1 -> 89.5 | Helped |
| Add filter normalization | ResNet20 · CIFAR-10 D | accuracy: 91.4 -> 91.5 | No clear effect |
| Add filter normalization | ResNet34 · ImageNet-1k highest contrast bin | accuracy: 63.3% -> 71.4% | Helped |
| Add filter normalization | ResNet34 · ExDark low light | accuracy: 28.3% -> 34.2% | Helped |
| Add filter normalization | ResNet18 · LEGUS NGC1313, trained on NGC628 | accuracy: 50.2% -> 51.9% | Helped |
| Add filter normalization | ResNet34 · ImageNet-P weather | Flip Rate: 41.3 -> 40.0 | Helped |
| Add gain-bias augmentation (maximum variation ±10%) (ablation) | ResNet20 · CIFAR-10 D_S | accuracy: 38.1 -> 76.9 | Helped |
| Use filter normalization instead of vanilla convolutions with gain-bias augmentation (ablation) | ResNet20 · CIFAR-10 D_S | accuracy: 76.9 -> 90.8 | Helped |
| Add soft weight-normalization regularization (ablation) | ResNet20 · CIFAR-10 D_S | accuracy: 38.1 -> 48.8 | Helped |
Surprising findings
- Vanilla R34 collapses from 73.3% to 2.1% on corrupted ImageNet sets, while CLIP-B only falls from about 60% to 14.3%.
- Learned first-layer filters of vanilla ResNets are skewed toward differencing, with many unnormalized filters that misclassify more often.
Limitations
- Gains on general corruptions (ImageNet-C) are small and mixed, with underperformance on some categories such as snow.
- Non-linearities break strict equivariance, so invariance is only approximate at the network level.
- Corrupted benchmarks are synthetic gain-bias perturbations that the method was designed for, so the comparison is tailored to its own design goal.
Experimental setup
Datasets: ImageNet-1k CIFAR-10 ExDark LEGUS
Benchmarks: ImageNet-1k corrupted sets D_C, D_L, D_B, D_S CIFAR-10 corrupted sets D_C, D_L, D_B, D_S ExDark LEGUS ImageNet-P ImageNet-C
Metrics: top-1 accuracy flip rate
Baselines: vanilla ResNet norm-equivariant networks (R20E) CLIP-B ViT-B ResNet101 instance normalization RandAugment AutoAugment
Builds on: batch normalization instance normalization norm-equivariant networks CLIP
Closest papers by meaning
- Normalization-Equivariant Neural Networks with Application to Image Denoising (NeurIPS 2023 · similarity 0.88)
- CNN Filter DB: An Empirical Investigation of Trained Convolutional Filters (CVPR 2022 · similarity 0.88)
- Filter Response Normalization Layer: Eliminating Batch Dependence in the Training of Deep Neural Networks (CVPR 2020 · similarity 0.88)
- DEALing with Image Reconstruction: Deep Attentive Least Squares (ICML 2025 · similarity 0.85)
- The Master Key Filters Hypothesis: Deep Filters Are General (AAAI 2025 · similarity 0.85)
- Deep Edge Filter: Return of the Human-Crafted Layer in Deep Learning (NeurIPS 2025 · similarity 0.85)
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