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Accurate approximations to density functionals have recently been obtainedvia machine learning (ML). By applying ML to a simple function of one variablewithout any random sampling, we extract the qualitative dependence of errors onhyperparameters. We find universal features of the behavior in extreme limits,including both very small and very large length scales, and the noise-freelimit. We show how such features arise in ML models of density functionals.

Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals