# Uniform convergence for Gaussian kernel ridge regression

arXiv: https://arxiv.org/abs/2508.11274 · HTML: https://mlsanity.com/paper/2508.11274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 3 of 3)

- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [On the Approximation of Kernel functions](https://mlsanity.com/paper/2403.06731/) (2024)

## Abstract (arXiv)

This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the L2-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where no such rates were previously known. In addition, we prove a polynomial L2-convergence rate in the case, where the Gaussian kernel's width parameter is fixed. This also contributes to the broader understanding of smooth kernels, for which previously only sub-polynomial L2-rates were known in similar settings. Together, these results provide new theoretical justification for the use of Gaussian KRR with fixed hyperparameters in nonparametric regression.