arXiv:2607.15922 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper provides a nontrivial boundedness framework for Fourier transforms when the input and output integrability exponents vary with position, including the endpoint regime where the input exponent tends to 1 and the output exponent tends to infinity. The transferable asset is the use of spatially varying modular norms together with logarithmic-Hölder regularity and finite-measure perturbations to retain a bounded transform. A practical neural-network use is a variable-exponent Fourier block whose normalization adapts to local signal complexity while constraining the exponent field to a mathematically safer family.
Replace a fixed-norm Fourier feature layer by a Fourier transform followed by spatially varying modular normalization. Use a baseline exponent approaching the endpoint regime at large coordinates and permit only bounded, smooth deviations so the transform remains controlled while the network can emphasize localized details.