{"ID":2823641,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24663","arxiv_id":"2512.24663","title":"Renormalization Group Guided Tensor Network Structure Search","abstract":"Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adaptivity, and optimization robustness across diverse tensor characteristics. They struggle with three key challenges: single-scale optimization missing multi-scale structures, discrete search spaces hindering smooth structure evolution, and separated structure-parameter optimization causing computational inefficiency. We propose RGTN (Renormalization Group guided Tensor Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows. Unlike fixed-scale discrete search methods, RGTN uses dynamic scale-transformation for continuous structure evolution across resolutions. Its core innovation includes learnable edge gates for optimization-stage topology modification and intelligent proposals based on physical quantities like node tension measuring local stress and edge information flow quantifying connectivity importance. Starting from low-complexity coarse scales and refining to finer ones, RGTN finds compact structures while escaping local minima via scale-induced perturbations. Extensive experiments on light field data, high-order synthetic tensors, and video completion tasks show RGTN achieves state-of-the-art compression ratios and runs 4-600$\\times$ faster than existing methods, validating the effectiveness of our physics-inspired approach.","short_abstract":"Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adap...","url_abs":"https://arxiv.org/abs/2512.24663","url_pdf":"https://arxiv.org/pdf/2512.24663v1","authors":"[\"Maolin Wang\",\"Bowen Yu\",\"Sheng Zhang\",\"Linjie Mi\",\"Wanyu Wang\",\"Yiqi Wang\",\"Pengyue Jia\",\"Xuetao Wei\",\"Zenglin Xu\",\"Ruocheng Guo\",\"Xiangyu Zhao\"]","published":"2025-12-31T06:31:43Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.AI\"]","methods":"[]","has_code":false}