  Tensor networks are efficient for extremely high-dimensional representation,
but their model selection, known as tensor network structure search (TN-SS), is
a challenging problem. Although several works have targeted TN-SS, most
existing algorithms are manually crafted heuristics with poor performance,
suffering from the curse of dimensionality and local convergence. In this work,
we jump out of the box, studying how to harness large language models (LLMs) to
automatically discover new TN-SS algorithms, replacing the involvement of human
experts. By observing how human experts innovate in research, we model their
common workflow and propose an automatic algorithm discovery framework called
tnGPS. The proposed framework is an elaborate prompting pipeline that instruct
LLMs to generate new TN-SS algorithms through iterative refinement and
enhancement. The experimental results demonstrate that the algorithms
discovered by tnGPS exhibit superior performance in benchmarks compared to the
current state-of-the-art methods.
