Emergent Mind
Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS
(2009.10683)
Published Sep 22, 2020
in
cs.LG
,
math.ST
,
stat.ML
,
and
stat.TH
Abstract
We prove that the reproducing kernel Hilbert spaces (RKHS) of a deep neural tangent kernel and the Laplace kernel include the same set of functions, when both kernels are restricted to the sphere $\mathbb{S}{d-1}$. Additionally, we prove that the exponential power kernel with a smaller power (making the kernel less smooth) leads to a larger RKHS, when it is restricted to the sphere $\mathbb{S}{d-1}$ and when it is defined on the entire $\mathbb{R}d$.
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