An Empirical Analysis of the Laplace and Neural Tangent Kernels

Autor:	Lencevicius, Ronaldas Paulius
Rok vydání:	2022
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Mathematics - Functional Analysis Mathematics - Statistics Theory 62M08 (Primary) 46C08 (Secondary) G.3
Zdroj:	California State University's ScholarWorks, Summer (2022)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 105 pages, 23 figures, to be published in California State University's ScholarWorks repository as part of master's degree completion
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.03761 Zobrazit plný text záznamu View this record from Arxiv