Discovering More Effective Tensor Network Structure Search Algorithms
  via Large Language Models (LLMs)
Junhua Zeng Guoxu Zhou Chao Li Zhun Sun Qibin Zhao
Tensor network structure search (TN-SS), aiming at searching for suitable
tensor network (TN) structures in representing high-dimensional problems,
largely promotes the efficacy of TN in various machine learning applications.
Nonetheless, finding a satisfactory TN structure using existing algorithms
remains challenging. To develop more effective algorithms and avoid the human
labor-intensive development process, we explore the knowledge embedded in large
language models (LLMs) for the automatic design of TN-SS algorithms. Our
approach, dubbed GPTN-SS, leverages an elaborate crafting LLM-based prompting
system that operates in an evolutionary-like manner. The experimental results,
derived from real-world data, demonstrate that GPTN-SS can effectively leverage
the insights gained from existing methods to develop novel TN-SS algorithms
that achieve a better balance between exploration and exploitation. These
algorithms exhibit superior performance in searching the high-quality TN
structures for natural image compression and model parameters compression while
also demonstrating generalizability in their performance.