Bilinear Bochner--Riesz Means on the Complex Sphere
arXiv:2608.25884
2026
Architecture
1 ideas extracted · analyzed Aug 29, 2026
What the math gives to ML
The paper develops bilinear spectral multipliers whose joint frequency response is a smooth truncated ball, and proves uniform boundedness on a complex sphere for a range of exponents and smoothness parameters. The transferable asset is not the sphere-specific harmonic-analysis proof itself, but a bilinear interaction layer that suppresses jointly high-frequency components while retaining interactions that are individually high-frequency but jointly low-frequency. This suggests a spectrally controlled bilinear module for spherical or graph neural networks, with the smoothness parameter providing an explicit knob for stability and aliasing suppression.
Ideas from this paper
Unverified
2026
Replace an unconstrained bilinear feature interaction with a joint spectral filter that only allows pairs of graph or spherical frequencies satisfying a soft radius constraint. The smooth factor attenuates interactions near and beyond the cutoff instead of making the hard low-pass decision used by ordinary spectral truncation, which should reduce high-frequency aliasing and unstable feature products.
Useful5/10
Difficulty6/10
Novelty6/10