  One of the most interesting problems in the recent renaissance of the studies
in kernel regression might be whether the kernel interpolation can generalize
well, since it may help us understand the `benign overfitting henomenon'
reported in the literature on deep networks. In this paper, under mild
conditions, we show that for any $\varepsilon>0$, the generalization error of
kernel interpolation is lower bounded by $\Omega(n^{-\varepsilon})$. In other
words, the kernel interpolation generalizes poorly for a large class of
kernels. As a direct corollary, we can show that overfitted wide neural
networks defined on the sphere generalize poorly.
