# Towards LLM-guided Efficient and Interpretable Multi-linear Tensor Network Rank Selection

arXiv: https://arxiv.org/abs/2410.10728 · HTML: https://mlsanity.com/paper/2410.10728/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Tensor-Train Recurrent Neural Networks for Video Classification](https://mlsanity.com/paper/1707.01786/) (2017)
- [LMPriors: Pre-Trained Language Models as Task-Specific Priors](https://mlsanity.com/paper/2210.12530/) (2022)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [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)
- [Moving Object Detection under Discontinuous Change in Illumination Using Tensor Low-Rank and Invariant Sparse Decomposition](https://mlsanity.com/paper/1904.03175/) (2019)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [tnGPS: Discovering Unknown Tensor Network Structure Search Algorithms via Large Language Models (LLMs)](https://mlsanity.com/paper/2402.02456/) (2024)

## Built on by (most cited first, 3 of 3)

- [TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs](https://mlsanity.com/paper/2501.15674/) (2025)
- [LLaVA-FA: Learning Fourier Approximation for Compressing Large Multimodal Models](https://mlsanity.com/paper/2602.00135/) (2026)
- [TeRA: Vector-based Random Tensor Network for High-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2509.03234/) (2025)

## Abstract (arXiv)

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs, our approach offers enhanced interpretability of the rank choices and can effectively optimise the objective function. This framework enables users without specialised domain expertise to utilise tensor network decompositions and understand the underlying rationale within the rank selection process. Experimental results validate our method on financial higher-order datasets, demonstrating interpretable reasoning, strong generalisation to unseen test data, and its potential for self-enhancement over successive iterations. This work is placed at the intersection of large language models and higher-order data analysis.