Generating Symbolic World Models via Test-time Scaling of Large Language Models

Zhouliang Yu, Yuhuan Yuan, Tim Z. Xiao, Fuxiang Frank Xia, Jie Fu, Ge Zhang, Ge lin, Weiyang Liu

Keywords: Symbolic World Model, LLM, Test-time Scaling

Abstract:

Solving complex planning problems requires Large Language Models (LLMs) to explicitly
model the state transition to avoid rule violations, comply with constraints, and ensure optimality—a task hindered by the inherent ambiguity of natural language. To overcome such
ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a
symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs
remains an open challenge due to the lack of PDDL training data. To address this challenge,
we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning
capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically,
we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling
approach to improve the quality of the initial solution and then refines the solution in a
fine-grained manner with verbalized machine learning. Our method outperforms o1-mini
by a considerable margin in the generation of PDDL domain, achieving over 50% success
rate on two tasks (i.e., generating PDDL domains from natural language description or
PDDL problems). This is done without requiring additional training. By taking advantage
of PDDL as state abstraction, our method is able to outperform current state-of-the-art
methods on almost all competition-level planning tasks.

Submission Number: 83