Predicting kernel regression learning curves from only raw data statistics

arXiv:2510.14878v3 Announce Type: replace-cross Abstract: We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoretical framework that predicts learning curves (test risk vs. sample size) from only two measurements: the empirical data covariance matrix and an empirical polynomial decomposition of the target function $f_*$. The key new idea is an analytical approximation of a kernel's eigenvalues and eigenfunctions with respect to an anisotropic data distribution. The eigenfunctions resemble Hermite polynomials o

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