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An Empirical Analysis of the Laplace and Neural Tangent Kernels
arXiv - MATH - Statistics Theory Pub Date : 2022-08-07 , DOI: arxiv-2208.03761 Ronaldas Paulius Lencevicius
arXiv - MATH - Statistics Theory Pub Date : 2022-08-07 , DOI: arxiv-2208.03761 Ronaldas Paulius Lencevicius
The neural tangent kernel is a kernel function defined over the parameter
distribution of an infinite width neural network. Despite the impracticality of
this limit, the neural tangent kernel has allowed for a more direct study of
neural networks and a gaze through the veil of their black box. More recently,
it has been shown theoretically that the Laplace kernel and neural tangent
kernel share the same reproducing kernel Hilbert space in the space of
$\mathbb{S}^{d-1}$ alluding to their equivalence. In this work, we analyze the
practical equivalence of the two kernels. We first do so by matching the
kernels exactly and then by matching posteriors of a Gaussian process.
Moreover, we analyze the kernels in $\mathbb{R}^d$ and experiment with them in
the task of regression.
更新日期：2022-08-09
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