Navigate Complex Physical Worlds via Geometrically Constrained LLM

AbstractThis study investigates the potential of Large Language Models (LLMs) for reconstructing and understanding the physical world based solely on textual knowledge. It explores the impact of model performance on spatial understanding abilities by introducing a set of geometric conventions and developing a workflow based on multi-layer graphs and multi-agent systems. The study examines how LLMs achieve multi-step and multi-objective geometric inference in a spatial environment, using unified geometric conventions and a graph-driven framework. A genetic algorithm, inspired by large-scale model knowledge, is employed to solve geometric constraint problems, enhancing the spatial reasoning capabilities of LLMs. This work innovatively explores the feasibility of using text-based LLMs as builders of the physical world and designs a workflow to enhance their spatial comprehension and construction capabilities.