# Resolution-Invariant Image Classification based on Fourier Neural Operators

arXiv: https://arxiv.org/abs/2304.01227 · HTML: https://mlsanity.com/paper/2304.01227/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Deep Fourier Up-Sampling](https://mlsanity.com/paper/2210.05171/) (2022)
- [Fine-to-coarse Knowledge Transfer For Low-Res Image Classification](https://mlsanity.com/paper/1605.06695/) (2016)
- [Convolutional Low-Resolution Fine-Grained Classification](https://mlsanity.com/paper/1703.05393/) (2017)

## Built on by (most cited first, 7 of 7)

- [Linearization Turns Neural Operators into Function-Valued Gaussian Processes](https://mlsanity.com/paper/2406.05072/) (2024)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Resolution-Robust 3D MRI Reconstruction with 2D Diffusion Priors: Diverse-Resolution Training Outperforms Interpolation](https://mlsanity.com/paper/2412.18584/) (2024)
- [A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media](https://mlsanity.com/paper/2402.11568/) (2024)
- [SONIC: Spectral Oriented Neural Invariant Convolutions](https://mlsanity.com/paper/2601.19884/) (2026)
- [Deep Psychovisual Image Representations](https://mlsanity.com/paper/2605.29260/) (2026)
- [A neural operator view on U-Nets for inverse imaging problems](https://mlsanity.com/paper/2608.05839/) (2026)

## Abstract (arXiv)

In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural networks to approximate operators between infinite dimensional function spaces. FNOs - which are neural operators with a specific parametrization - have been applied successfully in the context of parametric PDEs. We derive the FNO architecture as an example for continuous and Fr'echet-differentiable neural operators on Lebesgue spaces. We further show how CNNs can be converted into FNOs and vice versa and propose an interpolation-equivariant adaptation of the architecture.