A homogeneous geometry of low-rank tensors
Numerical Analysis
2026-01-01 v3 Numerical Analysis
Differential Geometry
Abstract
We consider sets of fixed CP, multilinear, and TT rank tensors, and derive conditions for when (the smooth parts of) these sets are smooth homogeneous manifolds. For CP and TT ranks, the conditions are essentially that the rank is sufficiently low. These homogeneous structures are then used to derive Riemannian metrics whose geodesics are both complete and efficient to compute.
Keywords
Cite
@article{arxiv.2512.13594,
title = {A homogeneous geometry of low-rank tensors},
author = {Simon Jacobsson},
journal= {arXiv preprint arXiv:2512.13594},
year = {2026}
}