Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning \textbf{Flows}. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.

本研究针对大型语言模型（LLMs）在生成详细准确的推理过程方面面临的挑战，提出了一种新颖的方法，即通过在线学习“Flows”生成高质量的推理过程以进行模型微调。通过使用在线直接偏好优化（DPO）学习，本方法展示了在数学推理任务中显著提高模型性能的潜力。

Flow-DPO：通过在线多代理学习提升大型语言模型的数学推理能力