Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Lin Chen; Sheng Xu

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arXiv · 2009.10683

Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Lin Chen·Sheng Xu

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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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cs.LG math.ST stat.ML stat.TH

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Lin Chen, Sheng Xu. 2020-09-22. Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS. https://arxiv.org/abs/2009.10683

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