mlsanityData to 7 Oct 2026

Resolution-Invariant Image Classification based on Fourier Neural Operators

arXiv 2304.01227 ↗First posted 2 Apr 2023cs.CV cs.LG cs.NAcited by 7

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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.

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

Builds on

11 of 26 references.

References · 11

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  4. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  7. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  8. 2021Global Filter Networks for Image Classificationcited by 257
  9. 2022Deep Fourier Up-Samplingcited by 27
  10. 2016Fine-to-coarse Knowledge Transfer For Low-Res Image Classificationcited by 11
  11. 2017Convolutional Low-Resolution Fine-Grained Classificationcited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 3.

7 papers.

  1. 2024Linearization Turns Neural Operators into Function-Valued Gaussian Processescited by 11
  2. 2025Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learningcited by 11
  3. 2024Resolution-Robust 3D MRI Reconstruction with 2D Diffusion Priors: Diverse-Resolution Training Outperforms Interpolationcited by 1
  4. 2024A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous mediacited by 0
  5. 2026SONIC: Spectral Oriented Neural Invariant Convolutionscited by 0
  6. 2026Deep Psychovisual Image Representationscited by 0
  7. 2026A neural operator view on U-Nets for inverse imaging problemscited by 0