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Large Dimensional Kernel Ridge Regression: Extending to Product Kernels

arXiv 2605.14524 ↗First posted 14 May 2026stat.ML cs.LGcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 20 of its 31 references that are in the map. First posted on arXiv 14 May 2026.

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References · 20

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2019Linearized two-layers neural networks in high dimensioncited by 155
  3. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  4. 2021Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regimecited by 95
  5. 2013Early stopping and non-parametric regression: An optimal data-dependent stopping rulecited by 86
  6. 2022Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regressioncited by 42
  7. 2023Generalization Ability of Wide Neural Networks on ℝcited by 28
  8. 2023Generalization in Kernel Regression Under Realistic Assumptionscited by 26
  9. 2018Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithmscited by 22
  10. 2024A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimatorcited by 22
  11. 2023On the Optimality of Misspecified Kernel Ridge Regressioncited by 20
  12. 2023On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decaycited by 19
8 more
  1. 2023Kernel interpolation generalizes poorlycited by 16
  2. 2022On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensionscited by 13
  3. 2024On the Saturation Effect of Kernel Ridge Regressioncited by 12
  4. 2024Universality of Kernel Random Matrices and Kernel Regression in the Quadratic Regimecited by 11
  5. 2023Optimal Rate of Kernel Regression in Large Dimensionscited by 10
  6. 2024Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensionscited by 9
  7. 2024The phase diagram of kernel interpolation in large dimensionscited by 9
  8. 2025Diagonal Over-parameterization in Reproducing Kernel Hilbert Spaces as an Adaptive Feature Model: Generalization and Adaptivitycited by 2

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