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arXiv · 2304.01227

Resolution-Invariant Image Classification based on Fourier Neural Operators

Samira Kabri·Tim Roith·Daniel Tenbrinck·Martin Burger
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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 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.

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Samira Kabri, Tim Roith, Daniel Tenbrinck, Martin Burger. 2023-04-02. Resolution-Invariant Image Classification based on Fourier Neural Operators. https://arxiv.org/abs/2304.01227

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