Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares
Abstract
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 over-parameterized, 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 alternating least square algorithm for tensor ring decomposition. The theoretical results are complemented by numerical experiments for both local minimum and one-loop convergence for the alternating least square algorithm.
Keywords
Cite
@article{arxiv.1905.07101,
title = {Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares},
author = {Ziang Chen and Yingzhou Li and Jianfeng Lu},
journal= {arXiv preprint arXiv:1905.07101},
year = {2020}
}