Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

09/22/2020

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by   Lin Chen, et al.

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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 𝕊^d-1. Additionally, we prove that the exponential power kernel with a smaller power (making the kernel more non-smooth) leads to a larger RKHS, when it is restricted to the sphere 𝕊^d-1 and when it is defined on the entire ℝ^d.