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:
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 $\mathbb{R}^d$.
Chat is not available.