# Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

arXiv: https://arxiv.org/abs/2009.10683 · HTML: https://mlsanity.com/paper/2009.10683/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2020.

## Built on by (most cited first, 30 of 74)

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## Abstract (arXiv)

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 mathbbSd-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 mathbbSd-1 and when it is defined on the entire ℝd.