Domain-Aware Tensor Network Structure Search
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912605667328000 |
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| author | Iacovides, Giorgos Zhou, Wuyang Li, Chao Zhao, Qibin Mandic, Danilo |
| author_facet | Iacovides, Giorgos Zhou, Wuyang Li, Chao Zhao, Qibin Mandic, Danilo |
| contents | Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art (SOTA) algorithms solve TN-SS as a purely numerical optimization problem and require extensive function evaluations, which is prohibitive for real-world applications. In addition, existing methods ignore the valuable domain information inherent in real-world tensor data and lack transparency in their identified TN structures. To this end, we propose a novel TN-SS framework, termed the tnLLM, which incorporates domain information about the data and harnesses the reasoning capabilities of large language models (LLMs) to directly predict suitable TN structures. The proposed framework involves a domain-aware prompting pipeline which instructs the LLM to infer suitable TN structures based on the real-world relationships between tensor modes. In this way, our approach is capable of not only iteratively optimizing the objective function, but also generating domain-aware explanations for the identified structures. Experimental results demonstrate that tnLLM achieves comparable TN-SS objective function values with much fewer function evaluations compared to SOTA algorithms. Furthermore, we demonstrate that the LLM-enabled domain information can be used to find good initializations in the search space for sampling-based SOTA methods to accelerate their convergence while preserving theoretical performance guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Domain-Aware Tensor Network Structure Search Iacovides, Giorgos Zhou, Wuyang Li, Chao Zhao, Qibin Mandic, Danilo Machine Learning Computation and Language Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art (SOTA) algorithms solve TN-SS as a purely numerical optimization problem and require extensive function evaluations, which is prohibitive for real-world applications. In addition, existing methods ignore the valuable domain information inherent in real-world tensor data and lack transparency in their identified TN structures. To this end, we propose a novel TN-SS framework, termed the tnLLM, which incorporates domain information about the data and harnesses the reasoning capabilities of large language models (LLMs) to directly predict suitable TN structures. The proposed framework involves a domain-aware prompting pipeline which instructs the LLM to infer suitable TN structures based on the real-world relationships between tensor modes. In this way, our approach is capable of not only iteratively optimizing the objective function, but also generating domain-aware explanations for the identified structures. Experimental results demonstrate that tnLLM achieves comparable TN-SS objective function values with much fewer function evaluations compared to SOTA algorithms. Furthermore, we demonstrate that the LLM-enabled domain information can be used to find good initializations in the search space for sampling-based SOTA methods to accelerate their convergence while preserving theoretical performance guarantees. |
| title | Domain-Aware Tensor Network Structure Search |
| topic | Machine Learning Computation and Language |
| url | https://arxiv.org/abs/2505.23537 |