Tangent Cones to TT Varieties
Optimization and Control
2017-05-30 v1 Machine Learning
Algebraic Geometry
Numerical Analysis
Abstract
As already done for the matrix case for example in [Joe Harris, Algebraic Geometry - A first course, p.256] we give a parametrization of the Bouligand tangent cone of the variety of tensors of bounded TT rank. We discuss how the proof generalizes to any binary hierarchical format. The parametrization can be rewritten as an orthogonal sum of TT tensors. Its retraction onto the variety is particularly easy to compose. We also give an implicit description of the tangent cone as the solution of a system of polynomial equations.
Keywords
Cite
@article{arxiv.1705.10152,
title = {Tangent Cones to TT Varieties},
author = {Benjamin Kutschan},
journal= {arXiv preprint arXiv:1705.10152},
year = {2017}
}