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• W3010803222 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." @default.
• W3010803222 created "2020-03-23" @default.
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• W3010803222 date "2019-05-16" @default.
• W3010803222 modified "2023-10-16" @default.
• W3010803222 title "Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares" @default.
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• W3010803222 doi "https://doi.org/10.48550/arxiv.1905.07101" @default.
• W3010803222 hasPublicationYear "2019" @default.
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