Gaussian kernels on non-simply-connected closed Riemannian manifolds are never positive definite
Not on the map. Why?
Abstract (arXiv)
We show that the Gaussian kernel expleft-λ dg2(bullet, bullet)right on any non-simply-connected closed Riemannian manifold (M,g), where dg is the geodesic distance, is not positive definite for any λ > 0, combining analyses in the recent preprint~[9] by Da Costa--Mostajeran--Ortega and classical comparison theorems in Riemannian geometry.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 7 of its 41 references that are in the map. First posted on arXiv 12 Mar 2023.
Builds on
7 of 41 references.
References · 7
- 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
- 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
- 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
- 2014Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernelscited by 30
- 2019Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Controlcited by 17
- 2020Dimension reduction in recurrent networks by canonicalizationcited by 11
- 2023The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circlecited by 5
Built on by
Citing papers per year: 2023: 2; 2024: 0; 2025: 0; 2026: 1.
3 papers.