Discovering More Effective Tensor Network Structure Search Algorithms via Large Language Models (LLMs)

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.