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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.22048 |
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Table of Contents:
- We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient conditions for these kernels to be strictly positive definite. This class of isotropic kernels is fairly general: First, it unifies stationary isotropic and dot product kernels, and second, it includes neural network kernels that arise from infinite-width limits of neural networks.