ICLR Poster Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Poster

Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Lin Chen · Sheng Xu

Keywords: [ neural tangent kernel ] [ Reproducing kernel Hilbert space ] [ Laplace kernel ] [ Singularity analysis ]

[ Abstract ] [ Paper PDF ]

[ Paper ]

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

S^{d - 1}

$\mathbb{S}^{d-1}$ . 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

S^{d - 1}

$\mathbb{S}^{d-1}$ and when it is defined on the entire

R^{d}

$\mathbb{R}^d$ .

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