# Renormalization Group Guided Tensor Network Structure Search

arXiv: https://arxiv.org/abs/2512.24663 · HTML: https://mlsanity.com/paper/2512.24663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 69 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 22 of 22)

- [Ansor: Generating High-Performance Tensor Programs for Deep Learning](https://mlsanity.com/paper/2006.06762/) (2020)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [AutoEmb: Automated Embedding Dimensionality Search in Streaming Recommendations](https://mlsanity.com/paper/2002.11252/) (2020)
- [AutoLoss: Automated Loss Function Search in Recommendations](https://mlsanity.com/paper/2106.06713/) (2021)
- [AutoMLP: Automated MLP for Sequential Recommendations](https://mlsanity.com/paper/2303.06337/) (2023)
- [AutoDenoise: Automatic Data Instance Denoising for Recommendations](https://mlsanity.com/paper/2303.06611/) (2023)
- [Low-tubal-rank Tensor Completion using Alternating Minimization](https://mlsanity.com/paper/1610.01690/) (2016)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluations](https://mlsanity.com/paper/2304.12875/) (2023)
- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [ERASE: Benchmarking Feature Selection Methods for Deep Recommender Systems](https://mlsanity.com/paper/2403.12660/) (2024)
- [Approximately Optimal Core Shapes for Tensor Decompositions](https://mlsanity.com/paper/2302.03886/) (2023)
- [Continuous Input Embedding Size Search For Recommender Systems](https://mlsanity.com/paper/2304.03501/) (2023)
- [Federated Knowledge Graph Completion via Latent Embedding Sharing and Tensor Factorization](https://mlsanity.com/paper/2311.10341/) (2023)
- [Domain-Aware Tensor Network Structure Search](https://mlsanity.com/paper/2505.23537/) (2025)
- [DNS-Rec: Data-aware Neural Architecture Search for Recommender Systems](https://mlsanity.com/paper/2402.00390/) (2024)
- [TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks](https://mlsanity.com/paper/1905.01331/) (2019)
- [DANCE: Resource-Efficient Neural Architecture Search with Data-Aware and Continuous Adaptation](https://mlsanity.com/paper/2507.04671/) (2025)

## 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.