Improving Rationality in the Reasoning Process of Language Models through Self-playing Game

Large language models (LLMs) have demonstrated considerable reasoning abilities in various tasks such as mathematics and coding. However, recent studies indicate that even the best models lack true comprehension of their reasoning processes. In this paper, we explore how self-play can enhance the rationality of models in the reasoning process without supervision from humans or superior models. We design a $\textit{\textbf{C}ritic-\textbf{D}iscernment \textbf{G}ame} (\textbf{CDG})$ in which a prover first provides a solution to a given problem and is subsequently challenged by critiques of its solution. These critiques either aim to assist or mislead the prover. The objective of the prover is to maintain the correct answer when faced with misleading comments, while correcting errors in response to constructive feedback. Our experiments on tasks involving mathematical reasoning, stepwise error detection, self-correction, and long-chain reasoning demonstrate that CDG training can significantly improve the ability of well-aligned LLMs to comprehend their reasoning process.