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We derive analytical expressions for the generalization performance of kernelregression as a function of the number of training samples using theoreticalmethods from Gaussian processes and statistical physics. Our expressions applyto wide neural networks due to an equivalence between training them and kernelregression with the Neural Tangent Kernel (NTK). By computing the decompositionof the total generalization error due to different spectral components of thekernel, we identify a new spectral principle: as the size of the training setgrows, kernel machines and neural networks fit successively higher spectralmodes of the target function. When data are sampled from a uniform distributionon a high-dimensional hypersphere, dot product kernels, including NTK, exhibitlearning stages where different frequency modes of the target function arelearned. We verify our theory with simulations on synthetic data and MNISTdataset.

Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks