Signed random Fourier features for fast density estimation with indefinite kernels

What the math gives to ML

The paper provides a constructive Monte Carlo factorization for translation-invariant kernels whose Fourier transform is signed rather than nonnegative. This is useful beyond KDE because many neural architectures implicitly require positive-definite random-feature kernels, excluding compact-support similarities and other indefinite interactions. The transferable asset is the signed spectral measure: sample frequencies from the absolute spectral density and carry a separate sign into the feature contraction, yielding linear-time approximations to indefinite pairwise aggregation. A promising neural use is replacing quadratic attention or graph message passing with a compact radial signed-kernel interaction, while explicitly testing whether signed cancellation improves locality or expressivity without destabilizing normalization.