Large Dimensional Kernel Ridge Regression: Extending to Product Kernels

arXiv:2605.14524v1 Announce Type: cross Abstract: Recent studies have reported extit{saturation effects} and extit{multiple 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 extit{minimax optimality} when the source condition sle 1; ii) the extit{saturation effect} when s>1; iii) a extit{periodic plateau phenomenon} in the convergence rate and a extit {multiple-descent behavior} with respect to the sample size n.

Source: arXiv cs.LG | 2026-05-15