Spectral Bounds for Kernel Quadrature
arXiv:2609.00553
2026
Memory
1 ideas extracted · analyzed Sep 2, 2026
What the math gives to ML
The paper identifies a concrete replacement for Monte Carlo random features: approximate the kernel's integral representation with a deterministic quadrature rule chosen to preserve the spectrum of the finite-data Gram matrix. The transferable asset is not merely cheaper kernel evaluation, but better control of the important eigenvalues, which govern conditioning, effective rank, regression accuracy, and optimization behavior. A practical neural-network-adjacent use is to build weighted deterministic Fourier or spherical feature layers, then compare their Gram-spectrum error and downstream accuracy against equal-width random features.
Ideas from this paper
✗ Failed on benchmark
2026
Replace random Fourier or random NTK features by a weighted deterministic quadrature rule for the kernel's feature integral. The resulting feature map uses the same linear-model interface as random features but can approximate the leading Gram-matrix eigenvalues substantially better at the same feature count, improving conditioning and reducing the width required for a target kernel approximation.
Useful7/10
Difficulty4/10
Novelty5/10