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PAC-FNO: Parallel-Structured All-Component Fourier Neural Operators for Recognizing Low-Quality Images
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Proposes PAC-FNO, a parallel all-component Fourier neural operator plug-in that lets a single model handle low-resolution and natural-corruption images for pretrained ImageNet classifiers, trained with a two-stage algorithm.
Problem
Pretrained image recognition models degrade sharply on images whose resolution differs from training and on natural input variations (fog, noise, compression), and existing fixes need multiple models per resolution or variation.
Approach
An FNO-based front-end without the ideal low-pass filter (all-component AC-FNO blocks), arranged in parallel branches and concatenated with a linear layer and batch norm, feeds a frozen-architecture pretrained backbone; a two-stage fine-tuning (target resolution first, then mixed low resolutions) yields one model for many resolutions and corruptions.
Key results
- On ImageNet-1k with ConvNeXt-Tiny at 32x32, PAC-FNO reaches 63.2% top-1 versus 34.5% for Resize, and the abstract claims improvements of up to 77.1% across resolutions.
- On ImageNet-C/P fog with ConvNeXt-Tiny at 32x32, PAC-FNO gets 30.4% versus 28.2% for Fine-tune (and about 7.6 points over Fine-tune on the 32x32 fog case reported in the text).
- PAC-FNO has 0.91M to 3.65M extra parameters, about 1-13% of backbone size, and is the only FNO variant that beats Fine-tune on fine-grained datasets at low resolution.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PAC-FNO instead of A-FNO | ResNet-18 · ImageNet-1k, 32×32 | top-1 accuracy: 49.5 -> 47.7 | Hurt |
| use PAC-FNO instead of FNO | Inception-V3 · ImageNet-1k, 32×32 | top-1 accuracy: 54.0 -> 54.9 | Helped |
| use PAC-FNO instead of A-FNO | ViT-B16 · ImageNet-1k, 32×32 | top-1 accuracy: 59.5 -> 52.1 | Hurt |
| use PAC-FNO instead of UNO | ConvNeXt-Tiny · ImageNet-1k, 32×32 | top-1 accuracy: 62.9 -> 63.2 | Helped |
| use PAC-FNO instead of the strongest listed baseline | ConvNeXt-Tiny · Oxford-IIIT Pets, 32×32 | top-1 accuracy | Helped |
| use PAC-FNO instead of Fine-tune | ConvNeXt-Tiny · Food-101, 32×32 | top-1 accuracy: 54.1 -> 77.8 | Helped |
| use PAC-FNO instead of Fine-tune | ConvNeXt-Tiny · ImageNet-C/P Fog, 32×32 | top-1 accuracy: 28.2 -> 30.4 | Helped |
| use PAC-FNO instead of UNO | ConvNeXt-Tiny · ImageNet-C/P Brightness, 32×32 | top-1 accuracy: 55.6 -> 56.5 | Helped |
| use PAC-FNO instead of UNO | ConvNeXt-Tiny · ImageNet-C/P Spatter, 32×32 | top-1 accuracy: 42.9 -> 46.0 | Helped |
| use PAC-FNO instead of UNO | ConvNeXt-Tiny · ImageNet-C/P Saturate, 32×32 | top-1 accuracy: 50.7 -> 56.5 | Helped |
| use parallel rather than serial AC-FNO blocks (ablation) | PAC-FNO with ConvNeXt-Tiny · ImageNet-1k, 224×224 | top-1 accuracy: 79.1 -> 81.5 | Helped |
| use parallel rather than serial AC-FNO blocks (ablation) | PAC-FNO with ConvNeXt-Tiny · ImageNet-C/P Fog, 224×224 | top-1 accuracy: 48.0 -> 62.8 | Helped |
Surprising findings
- Removing the ideal low-pass filter (keeping all frequency components) is argued to matter for fine-grained classification, where FNO-style variants with low-pass filters underperform Fine-tune.
- Super-resolution baselines (DRLN, DRPN) collapse under input variations such as fog, despite working on clean low-resolution images.
Limitations
- Evaluated only on single degradations; combined degradations (e.g., low resolution plus fog plus blur) are left to future work.
- At target resolution PAC-FNO can be slightly below Resize or Fine-tune (e.g., 81.5 vs 82.5 on ImageNet-1k with ConvNeXt-Tiny).
Experimental setup
Datasets: ImageNet-1k Stanford Cars Oxford-IIIT Pets Flowers FGVC Aircraft Food-101 ImageNet-C/P
Benchmarks: ImageNet-1k Stanford Cars Oxford-IIIT Pets Flowers FGVC Aircraft Food-101 ImageNet-C/P (fog, brightness, spatter, saturate)
Metrics: top-1 accuracy relative accuracy
Baselines: Resize Fine-tune DRLN DRPN FNO UNO A-FNO OSRT
Builds on: Fourier neural operator U-shaped FNO adaptive FNO (A-FNO)
Closest papers by meaning
- Neural Operators with Localized Integral and Differential Kernels (ICML 2024 · similarity 0.84)
- Amortized Fourier Neural Operators (NeurIPS 2024 · similarity 0.83)
- DiffFNO: Diffusion Fourier Neural Operator (CVPR 2025 · similarity 0.83)
- Multilinear Operator Networks (ICLR 2024 · similarity 0.83)
- Component Fourier Neural Operator for Singularly Perturbed Differential Equations (AAAI 2024 · similarity 0.82)
- Mechanistic Interpretability with Sparse Autoencoder Neural Operators (NeurIPS 2026 · similarity 0.82)
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