Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHSDownload PDF

28 Sept 2020, 15:49 (edited 18 Mar 2021)ICLR 2021 PosterReaders: Everyone
  • 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 $\mathbb{R}^d$.
  • One-sentence Summary: We prove that the reproducing kernel Hilbert spaces of a deep neural tangent kernel and the Laplace kernel include the same set of functions.
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