An Empirical Analysis of the Laplace and Neural Tangent Kernels
This work provides empirical insights into kernel methods for researchers in machine learning theory, though it is incremental as it builds on prior theoretical findings.
The paper investigates the practical equivalence between the Laplace and neural tangent kernels, showing they can be matched exactly and through Gaussian process posteriors, with experiments in regression tasks.
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.