Abstract
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 Fréchet-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.
This work was supported by the European Union’s Horizon 2020 programme, Marie Skłodowska-Curie grant agreement No. 777826. TR and MB acknowledge the support of the BMBF, grant agreement No. 05M2020. SK and MB acknowledge the support of the DFG, project BU 2327/19-1. This work was carried out while MB was with the FAU Erlangen-Nürnberg.
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Notes
- 1.
Our code is available online: github.com/samirak98/FourierImaging.
- 2.
This dataset consists of 60, 000 training and 10, 000 test \(28\times 28\) images (grayscale).
- 3.
We employ a former version of the data set, which consists of 76, 262 RGB images for training and 2, 250 images for testing of size \(224\times 224\), where the task is to classify birds out of 450 possible classes.
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Kabri, S., Roith, T., Tenbrinck, D., Burger, M. (2023). Resolution-Invariant Image Classification Based on Fourier Neural Operators. In: Calatroni, L., Donatelli, M., Morigi, S., Prato, M., Santacesaria, M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2023. Lecture Notes in Computer Science, vol 14009. Springer, Cham. https://doi.org/10.1007/978-3-031-31975-4_18
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