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Fourier-basis Functions to Bridge Augmentation Gap: Rethinking Frequency Augmentation in Image Classification
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Proposes Auxiliary Fourier-basis Augmentation (AFA), which adds weighted Fourier-basis sinusoids per RGB channel as an adversarial-style augmentation with parallel batch norm and an auxiliary cross-entropy loss, to improve corruption robustness, OOD generalization, and consistency on image classification.
Problem
Visual augmentations leave gaps in frequency-domain robustness, so classifiers remain vulnerable to corruptions and perturbations at frequencies not covered by training augmentations, while existing frequency or adversarial augmentations are computationally expensive.
Approach
Generate adversarial-style augmentations by adding randomly sampled Fourier-basis planar waves (random frequency, direction, and exponentially distributed strength per channel) without gradient-based optimization, and train them through an auxiliary branch with parallel batch normalization and an averaged cross-entropy (ACE) loss, complementing visual augmentations such as AugMix, PRIME, and Trivi
Key results
- On ImageNet with ResNet-18, AugMix+AFA (ACE) improves standard accuracy by 1.6% and robust accuracy by 4.1% (mCE 5.6% lower) over AugMax.
- AFA combined with PRIME on ImageNet ResNet-50 raises robustness accuracy on IN-C from 49.2 to 53.9 while mCE drops from 64.9 to 59.2.
- AFA requires about 1.62x memory and 2x FLOPs of standard augmentation training, versus 2.35x memory and 8x FLOPs for AugMax with 5 PGD steps.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add AFA to AugMix using ACE loss | ResNet-18 · ImageNet | SA: 65.2 -> 68.1 | Helped |
| Add AFA to AugMix using ACE loss | ResNet-18 · ImageNet | RA: 31.5 -> 41.1 | Helped |
| Add AFA to AugMix using ACE loss | ResNet-18 · ImageNet | mCE: 87.1 -> 75.0 | Helped |
| Add AFA to PRIME | CCT · ImageNet-C | RA: 54.1 -> 58.7 | Helped |
| Add AFA to PRIME | CCT · ImageNet-¯C | RA: 54.5 -> 61.2 | Helped |
| Add AFA to PRIME | CCT · ImageNet-R | accuracy: 39.2 -> 43.2 | Helped |
| Add AFA to PRIME | CCT · ImageNet-P | mFP: 36.1 -> 31.9 | Helped |
| Add AFA to PRIME | ResNet-18 · C10-C | RA: 89.81 -> 90.64 | Helped |
| Add AFA to PRIME | ResNet-18 · C100-C | RA: 66.16 -> 68.48 | Helped |
| Use AFA in the auxiliary component rather than only in the main component (ablation) | ResNet-18 · C10 | RA: 83.25 -> 88.22 | Helped |
| Use AFA in the auxiliary component rather than only in the main component (ablation) | ResNet-18 · C10 | SA: 92.36 -> 94.69 | Helped |
| Use AFA in the auxiliary component rather than only in the main component (ablation) | ResNet-18 · C100 | RA: 58.70 -> 62.53 | Helped |
Surprising findings
- Using the JSD loss with AFA did not significantly improve robustness over the simpler ACE loss, despite higher computational cost.
- Training with AFA alone (no visual augmentation) on ResNet-18 can improve C10-C robustness accuracy from 73.67 to 88.22.
Limitations
- Fourier-basis augmented images look unnatural and their benefit depends on the auxiliary branch design (without it, SA and RA degrade)
- Improvements on IN-3DCC are less pronounced because 3D geometric corruptions are more complex transformations
- Gains in standard accuracy are not uniform; some combinations (e.g., AugMix with AFA on CIFAR-100) show small drops
Experimental setup
Datasets: CIFAR-10 CIFAR-100 TinyImageNet ImageNet
Benchmarks: C10-C C100-C TIN-C IN-C IN-̄C IN-3DCC IN-R IN-v2 IN-P
Metrics: standard accuracy robustness accuracy mean corruption error mean flip rate mean top-5 distance average accuracy
Baselines: AugMax AugMix PRIME TrivialAugment APR-SP AugSVF
Builds on: AugMax AugMix PRIME TrivialAugment
Closest papers by meaning
- A Fourier Perspective on Model Robustness in Computer Vision (NeurIPS 2019 · similarity 0.90)
- D-GAP: Improving Out-of-Domain Robustness via Dataset-Agnostic and Gradient-Guided Augmentation in Amplitude and Pixel Spaces (NeurIPS 2026 · similarity 0.88)
- CutFreq: Cut-and-Swap Frequency Components for Low-Level Vision Augmentation (AAAI 2024 · similarity 0.87)
- Robust Image Denoising through Adversarial Frequency Mixup (CVPR 2024 · similarity 0.85)
- Generalizable Fourier Augmentation for Unsupervised Video Object Segmentation (AAAI 2024 · similarity 0.85)
- Misalignment-Robust Frequency Distribution Loss for Image Transformation (CVPR 2024 · similarity 0.84)
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