Resolution-Invariant Image Classification based on Fourier Neural Operators
This work addresses image classification challenges for varying resolutions, but it appears incremental as it adapts existing FNO methods to a new application without reporting performance gains.
The paper tackles the problem of resolution-invariant image classification by adapting Fourier Neural Operators (FNOs) from parametric PDEs to this task, showing how to convert between FNOs and CNNs and proposing an interpolation-equivariant architecture.
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.