Nash CoT: Multi-Path Inference with Preference Equilibrium

Chain-of-thought (CoT) prompting has emerged as a powerful technique for enhancing the reasoning capabilities of LLMs on complex problems. Among CoT-related studies, self-consistency (Multi-path inference with answer filtering through voting) involves generating multiple reasoning paths using the CoT framework and then selecting the most frequently produced outputs standing out as a concise yet competitive approach. While self-consistency has indeed led to the improvements in LLM inference, the use of multi-path inference also escalates deployment costs. Therefore, maintaining the performance benefits of self-consistency inherited from multi-path inference while reducing the inference costs holds significant value. In this research, we conceptualize language decoding as a preference consensus game, constructing a bi-player gaming system within each local path, and introduce Nash Chain-of-Thought (Nash CoT). Specifically, for a given question, we leverage LLM to autonomously select the contextually relevant template and generate outputs guided by this template, aiming to reach Nash Equilibrium alongside normal generation in each path. This approach allows us to achieve comparable or improved performance compared to self-consistency while using fewer inference paths on various inference tasks, including Arabic reasoning, Commonsense Question answering, and Symbolic inference.