Solving Mystery Planning Problems Using Category Theory, Functors, and Large Language Models

Large language models (LLMs) have shown remarkable capabilities in natural language understanding and generation. However, they face challenges in solving complex planning problems, especially those obscured by altered terminologies and representations, known as mystery planning problems. This paper presents a novel approach leveraging category theory and functors to systematically map mystery planning problems to their canonical forms, enabling effective planning solutions. We demonstrate our methodology using the Mystery Blocks World domain, showcasing significant improvements in planning accuracy and efficiency. Contemporary LLMs, such as GPT-4 and Claude-3.5 Sonnet, conjecture the canonical form and the corresponding functor only by observing the structure of the mystery planning problem, and the resulting approach improves the accuracy of the LLM-based planning solution to 60% for problems with 4 blocks.