An Empirical Analysis of the Laplace and Neural Tangent Kernels
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911196197683200 |
|---|---|
| author | Lencevičius, Ronaldas Paulius |
| author_facet | Lencevičius, Ronaldas Paulius |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_03761 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Empirical Analysis of the Laplace and Neural Tangent Kernels Lencevičius, Ronaldas Paulius Machine Learning Functional Analysis Statistics Theory 62M08 (Primary), 46C08 (Secondary) G.3 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. |
| title | An Empirical Analysis of the Laplace and Neural Tangent Kernels |
| topic | Machine Learning Functional Analysis Statistics Theory 62M08 (Primary), 46C08 (Secondary) G.3 |
| url | https://arxiv.org/abs/2208.03761 |