Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS
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 $\mathbb{R}^d$.
Cite
Text
Chen and Xu. "Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS." International Conference on Learning Representations, 2021.Markdown
[Chen and Xu. "Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS." International Conference on Learning Representations, 2021.](https://mlanthology.org/iclr/2021/chen2021iclr-deep/)BibTeX
@inproceedings{chen2021iclr-deep,
title = {{Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS}},
author = {Chen, Lin and Xu, Sheng},
booktitle = {International Conference on Learning Representations},
year = {2021},
url = {https://mlanthology.org/iclr/2021/chen2021iclr-deep/}
}