  The generalization ability of kernel interpolation in large dimensions (i.e.,
$n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting
problems in the recent renaissance of kernel regression, since it may help us
understand the 'benign overfitting phenomenon' reported in the neural networks
literature. Focusing on the inner product kernel on the sphere, we fully
characterized the exact order of both the variance and bias of
large-dimensional kernel interpolation under various source conditions $s\geq
0$. Consequently, we obtained the $(s,\gamma)$-phase diagram of
large-dimensional kernel interpolation, i.e., we determined the regions in
$(s,\gamma)$-plane where the kernel interpolation is minimax optimal,
sub-optimal and inconsistent.
