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

• URL: http://arxiv.org/abs/2305.14912v5
• Date: Fri, 5 Apr 2024 09:42:14 GMT
• Title: SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective
• Authors: Yu-Bang Zheng, Xi-Le Zhao, Junhua Zeng, Chao Li, Qibin Zhao, Heng-Chao Li, Ting-Zhu Huang,
• Abstract summary: 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. 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.
• Score: 41.62808372395741
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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