I've been dabbling in using Fourier analysis in deep learning lately, and I'm surprised it that I haven't turned up very much research in this area (Fourier Neural Operators being what seems to be the biggest exception). Fourier analysis is such a ubiquitous tool, intuitively I'd think it would work great for deep learning. My suspicion has been that complex numbers are difficult to work with, and maybe I'm just bad at surfacing the relevant research, but I'd be interested to hear from those better informed. (My naive approach has been to simply concatenate the real and complex components together into an n+1 dimensional tensor, but surely there's a way that better respects the structure of complex numbers.)
Might be useful to use gabor filters as the basis function, since just 2d cosine filters doesn't produce particularly sparse output for angled features. The additional overcompleteness would probably be helpful for the NN learning.
A fun little bit of trivia: Mammalian brains implement Gabor filters in the primary visual cortex (V1), as the first step of the visual processing pipeline.
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There's also 2D rope for ViT, but I don't know how it works exactly.