# Large Dimensional Kernel Ridge Regression: Extending to Product Kernels

arXiv: https://arxiv.org/abs/2605.14524 · HTML: https://mlsanity.com/paper/2605.14524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 20 of 20)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime](https://mlsanity.com/paper/2105.15004/) (2021)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression](https://mlsanity.com/paper/2204.10425/) (2022)
- [Generalization Ability of Wide Neural Networks on ℝ](https://mlsanity.com/paper/2302.05933/) (2023)
- [A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator](https://mlsanity.com/paper/2403.08938/) (2024)
- [Generalization in Kernel Regression Under Realistic Assumptions](https://mlsanity.com/paper/2312.15995/) (2023)
- [Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms](https://mlsanity.com/paper/1801.07226/) (2018)
- [On the Optimality of Misspecified Kernel Ridge Regression](https://mlsanity.com/paper/2305.07241/) (2023)
- [On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay](https://mlsanity.com/paper/2309.13337/) (2023)
- [Kernel interpolation generalizes poorly](https://mlsanity.com/paper/2303.15809/) (2023)
- [On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensions](https://mlsanity.com/paper/2205.13525/) (2022)
- [On the Saturation Effect of Kernel Ridge Regression](https://mlsanity.com/paper/2405.09362/) (2024)
- [Universality of Kernel Random Matrices and Kernel Regression in the Quadratic Regime](https://mlsanity.com/paper/2408.01062/) (2024)
- [Optimal Rate of Kernel Regression in Large Dimensions](https://mlsanity.com/paper/2309.04268/) (2023)
- [Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions](https://mlsanity.com/paper/2401.01270/) (2024)
- [The phase diagram of kernel interpolation in large dimensions](https://mlsanity.com/paper/2404.12597/) (2024)
- [Diagonal Over-parameterization in Reproducing Kernel Hilbert Spaces as an Adaptive Feature Model: Generalization and Adaptivity](https://mlsanity.com/paper/2501.08679/) (2025)

## Abstract (arXiv)

Recent studies have reported textitsaturation effects and textitmultiple descent behavior in large dimensional kernel ridge regression (KRR). However, these findings are predominantly derived under restrictive settings, such as inner product kernels on sphere or strong eigenfunction assumptions like hypercontractivity. Whether such behaviors hold for other kernels remains an open question. In this paper, we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previously associated with inner product kernels on sphere, including: i) the textitminimax optimality when the source condition s≤ 1; ii) the textitsaturation effect when s>1; iii) a textitperiodic plateau phenomenon in the convergence rate and a textit multiple-descent behavior with respect to the sample size n.