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Renormalization Group Guided Tensor Network Structure Search

arXiv 2512.24663 ↗First posted 31 Dec 2025cs.CV cs.AIcited by 0

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Abstract (arXiv)

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× faster than existing methods, validating the effectiveness of our physics-inspired approach.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 69 references that are in the map. First posted on arXiv 31 Dec 2025.

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References · 22

  1. 2020Ansor: Generating High-Performance Tensor Programs for Deep Learningcited by 199
  2. 2016Tensor Ring Decompositioncited by 125
  3. 2014Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determinationcited by 65
  4. 2019Tree Tensor Networks for Generative Modelingcited by 63
  5. 2017Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectivescited by 53
  6. 2018Neural Network Renormalization Groupcited by 48
  7. 2020AutoEmb: Automated Embedding Dimensionality Search in Streaming Recommendationscited by 47
  8. 2021AutoLoss: Automated Loss Function Search in Recommendationscited by 31
  9. 2023AutoMLP: Automated MLP for Sequential Recommendationscited by 25
  10. 2023AutoDenoise: Automatic Data Instance Denoising for Recommendationscited by 23
  11. 2016Low-tubal-rank Tensor Completion using Alternating Minimizationcited by 18
  12. 2022Permutation Search of Tensor Network Structures via Local Samplingcited by 13
10 more
  1. 2023Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluationscited by 12
  2. 2023SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspectivecited by 9
  3. 2024ERASE: Benchmarking Feature Selection Methods for Deep Recommender Systemscited by 9
  4. 2023Approximately Optimal Core Shapes for Tensor Decompositionscited by 8
  5. 2023Continuous Input Embedding Size Search For Recommender Systemscited by 7
  6. 2023Federated Knowledge Graph Completion via Latent Embedding Sharing and Tensor Factorizationcited by 5
  7. 2025Domain-Aware Tensor Network Structure Searchcited by 5
  8. 2024DNS-Rec: Data-aware Neural Architecture Search for Recommender Systemscited by 4
  9. 2019TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networkscited by 3
  10. 2025DANCE: Resource-Efficient Neural Architecture Search with Data-Aware and Continuous Adaptationcited by 2

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