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arXiv · 2305.14912

SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective

Yu-Bang Zheng·Xi-Le Zhao·Junhua Zeng·Chao Li·Qibin Zhao·Heng-Chao Li·Ting-Zhu Huang
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Abstract

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard problem. Recent "sampling-evaluation"-based methods require sampling an extensive collection of structures and evaluating them one by one, resulting in prohibitively high computational costs. To address this issue, we propose a novel TN paradigm, named SVD-inspired TN decomposition (SVDinsTN), which allows us to efficiently solve the TN-SS problem from a regularized modeling perspective, eliminating the repeated structure evaluations. To be specific, by inserting a diagonal factor for each edge of the fully-connected TN, SVDinsTN allows us to calculate TN cores and diagonal factors simultaneously, with the factor sparsity revealing a compact TN structure. In theory, we prove a convergence guarantee for the proposed method. Experimental results demonstrate that the proposed method achieves approximately 100 to 1000 times acceleration compared to the state-of-the-art TN-SS methods while maintaining a comparable level of representation ability.

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Yu-Bang Zheng, Xi-Le Zhao, Junhua Zeng, Chao Li, Qibin Zhao, Heng-Chao Li, Ting-Zhu Huang. 2023-05-24. SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective. https://arxiv.org/abs/2305.14912

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