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arXiv · 1905.07101

Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares

Ziang Chen·Yingzhou Li·Jianfeng Lu
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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.

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Ziang Chen, Yingzhou Li, Jianfeng Lu. 2019-05-17. Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares. https://arxiv.org/abs/1905.07101

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