CoTEvol：用于数学推理数据合成的自演化思维链
CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning
AI总结：
本文提出CoTEvol，一种基于遗传算法的思维链生成框架，通过全局交叉和局部突变提升生成准确性和多样性，实验表明其在数学推理任务中效果优于传统方法。
摘要：
大型语言模型（LLMs）在高质量思维链（CoT）训练下表现出强大的数学推理能力，但昂贵的CoT人工标注阻碍了进一步发展。现有解决方案如从更强LLMs进行知识蒸馏或基于测试时搜索的自我生成方法，常存在边际效益递减或计算开销大等问题。本文提出CoTEvol，一种遗传进化框架，将CoT生成视为基于推理轨迹的群体搜索问题。候选轨迹通过轨迹层面的反思全局交叉和步骤层面的不确定性引导局部突变进行迭代进化，实现整体重组和精细优化。设计轻量级、任务感知的适应度函数以引导进化过程向准确且多样的推理方向发展。实验表明，CoTEvol将正确CoT生成的成功率提高超过30%，并增强了结构多样性，效率显著提升。训练于这些进化CoT数据的LLMs在八个数学基准测试中平均提升6.6%，优于先前的知识蒸馏和自我生成方法。这些结果证明了进化CoT生成作为数学推理任务可扩展且有效方法的潜力。
英文摘要：
Large Language Models (LLMs) exhibit strong mathematical reasoning when trained on high-quality Chain-of-Thought (CoT) that articulates intermediate steps, yet costly CoT curation hinders further progress. While existing remedies such as distillation from stronger LLMs and self-synthesis based on test-time search alleviate this issue, they often suffer from diminishing returns or high computing overhead.In this work, we propose CoTEvol, a genetic evolutionary framework that casts CoT generation as a population-based search over reasoning trajectories.Candidate trajectories are iteratively evolved through reflective global crossover at the trajectory level and local mutation guided by uncertainty at the step level, enabling holistic recombination and fine-grained refinement. Lightweight, task-aware fitness functions are designed to guide the evolutionary process toward accurate and diverse reasoning. Empirically, CoTEvol improves correct-CoT synthesis success by over 30% and enhances structural diversity, with markedly improved efficiency. LLMs trained on these evolutionary CoT data achieve an average gain of 6.6% across eight math benchmarks, outperforming previous distillation and self-synthesis approaches. These results underscore the promise of evolutionary CoT synthesis as a scalable and effective method for mathematical reasoning tasks.
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