Tensor ring decomposition: Optimization landscape and one-loop convergence of alternating least squares

Published

Journal Article

© 2020 Society for Industrial and Applied Mathematics. In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the existence of spurious local minima for the optimization landscape even when the tensor ring format is much overparameterized, i.e., with bond dimension much larger than that of the true target tensor. On the other hand, when the bond dimension is further increased, we establish one-loop convergence for the alternating least squares algorithm for the tensor ring decomposition. The theoretical results are complemented by numerical experiments for both local minima and the one-loop convergence for the alternating least squares algorithm.

Full Text

Duke Authors

Cited Authors

  • CHEN, Z; LI, Y; LU, J

Published Date

  • January 1, 2020

Published In

Volume / Issue

  • 41 / 3

Start / End Page

  • 1416 - 1442

Electronic International Standard Serial Number (EISSN)

  • 1095-7162

International Standard Serial Number (ISSN)

  • 0895-4798

Digital Object Identifier (DOI)

  • 10.1137/19M1270689

Citation Source

  • Scopus