5/20/2026
at
2:44:48 PM
There have been some interesting advances in trying to add spectral information to the data that a learning architecture has at its disposal, but there are a couple roadblocks that I don’t think have been solved yet.1. Complex-valued NNs are not an easy generalization of real ones.
2. A localization in one domain implies non-local behavior in the other (this is the Fourier uncertainty principle).
Fourier Neural Operators (FNOs) come close to what I want to see in this area but since they enforce sparsity in the spectral domain their application is necessarily limited.
by TimorousBestie
5/20/2026
at
3:33:35 PM
I do wonder if a wavelet transform might be better.
by FuckButtons
5/20/2026
at
4:58:19 PM
I think one can do better with a wavelet, shearlet, or curvelet transform that is adapted to the problem domain at hand. But the uncertainty principle still haunts those transforms, and anyway the goal is to be domain-agile.
by TimorousBestie