Nash CoT: Multi-Path Inference with Preference Equilibrium

Chain of thought (CoT) is a reasoning framework that can enhance the performance of Large Language Models (LLMs) on complex inference tasks. In particular, among various studies related to CoT, multi-path inference stands out as a simple yet effective improvement. However, there is no optimal setting for the number of inference paths. Therefore, we have to increase the number of inference paths to obtain better results, which in turn increases the inference cost. To address this limitation, we can utilize question-related role templates to guide LLMs into relevant roles, thereby increasing the possibility of correct inferences for each path and further reducing dependence on the number of inference paths while improving reasoning accuracy. However, placing LLMs into specific roles may reduce their reasoning diversity and performance on a few tasks where role dependence is low. To alleviate the excessive immersion of the LLM into a specific role, we propose Nash CoT by constructing a competitive system on each path that balances the generation from role-specific LLMs' and the general LLMs' generation, thereby ensuring both effective role adoption and diversity in LLM generation further maintaining the performance of multi-path inference while reducing the requirement of the number of inference paths. We evaluate Nash CoT across various inference tasks, including Arabic Reasoning, Commonsense Question Answering, and Symbolic Inference, achieving results that are comparable to or better than those of multi-path CoT with the equal number of inference paths.