Resolution-Invariant Image Classification based on Fourier Neural Operators

• URL: http://arxiv.org/abs/2304.01227v1
• Date: Sun, 2 Apr 2023 10:23:36 GMT
• Title: Resolution-Invariant Image Classification based on Fourier Neural Operators
• Authors: Samira Kabri, Tim Roith, Daniel Tenbrinck, Martin Burger
• Abstract summary: We investigate the use of generalization Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs) We derive the FNO architecture as an example for continuous and Fr'echet-differentiable neural operators on Lebesgue spaces.
• Score: 1.3190581566723918
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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