The generalization error curve of certain kernel regression method aims at
determining the exact order of generalization error with various source
condition, noise level and choice of the regularization parameter rather than
the minimax rate. In this work, under mild assumptions, we rigorously provide a
full characterization of the generalization error curves of the kernel gradient
descent method (and a large class of analytic spectral algorithms) in kernel
regression. Consequently, we could sharpen the near inconsistency of kernel
interpolation and clarify the saturation effects of kernel regression
algorithms with higher qualification, etc. Thanks to the neural tangent kernel
theory, these results greatly improve our understanding of the generalization
behavior of training the wide neural networks. A novel technical contribution,
the analytic functional argument, might be of independent interest.

通过分析核回归方法的泛化误差曲线，提供了大量分析谱算法和核梯度下降方法的泛化误差曲线的全面特征描述，进而深化了核插值的不一致性和高资格核回归算法的饱和效应等的理解，这些结果极大地改善了我们对训练宽神经网络泛化行为的认识。值得独立关注的新技术贡献是分析函数论证。