# PAC-FNO: Parallel-Structured All-Component Fourier Neural Operators for Recognizing Low-Quality Images

arXiv: https://arxiv.org/abs/2402.12721 · HTML: https://mlsanity.com/paper/2402.12721/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Deep Back-Projection Networks For Super-Resolution](https://mlsanity.com/paper/1803.02735/) (2018)
- [Densely Residual Laplacian Super-Resolution](https://mlsanity.com/paper/1906.12021/) (2019)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [OSRT: Omnidirectional Image Super-Resolution with Distortion-aware Transformer](https://mlsanity.com/paper/2302.03453/) (2023)
- [Convolutional Low-Resolution Fine-Grained Classification](https://mlsanity.com/paper/1703.05393/) (2017)

## Built on by (most cited first, 4 of 4)

- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [Smoothing-Based Conformal Prediction for Balancing Efficiency and Interpretability](https://mlsanity.com/paper/2509.22529/) (2025)
- [Snapshot 3D image projection using a diffractive decoder](https://mlsanity.com/paper/2512.20464/) (2025)

## Abstract (arXiv)

A standard practice in developing image recognition models is to train a model on a specific image resolution and then deploy it. However, in real-world inference, models often encounter images different from the training sets in resolution and/or subject to natural variations such as weather changes, noise types and compression artifacts. While traditional solutions involve training multiple models for different resolutions or input variations, these methods are computationally expensive and thus do not scale in practice. To this end, we propose a novel neural network model, parallel-structured and all-component Fourier neural operator (PAC-FNO), that addresses the problem. Unlike conventional feed-forward neural networks, PAC-FNO operates in the frequency domain, allowing it to handle images of varying resolutions within a single model. We also propose a two-stage algorithm for training PAC-FNO with a minimal modification to the original, downstream model. Moreover, the proposed PAC-FNO is ready to work with existing image recognition models. Extensively evaluating methods with seven image recognition benchmarks, we show that the proposed PAC-FNO improves the performance of existing baseline models on images with various resolutions by up to 77.1% and various types of natural variations in the images at inference.