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arXiv · 2504.19981

Accurate and Diverse LLM Mathematical Reasoning via Automated PRM-Guided GFlowNets

Adam Younsi·Ahmed Attia·Abdalgader Abubaker·Mohamed El Amine Seddik·Hakim Hacid·Salem Lahlou
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Abstract

Achieving both accuracy and diverse reasoning remains challenging for Large Language Models (LLMs) in complex domains like mathematics. A key bottleneck is evaluating intermediate reasoning steps to guide generation without costly human annotations. To address this, we first introduce a novel Process Reward Model (PRM) trained automatically using Monte Carlo Tree Search coupled with a similarity-based data augmentation technique, effectively capturing step-level reasoning quality. Leveraging this PRM, we then adapt Generative Flow Networks (GFlowNets) to operate at the reasoning step level. Unlike traditional reinforcement learning focused on maximizing a single reward, GFlowNets naturally sample diverse, high-quality solutions proportional to their rewards, as measured by our PRM. Empirical evaluation shows strong improvements in both accuracy and solution diversity on challenging mathematical benchmarks (e.g., +2.59% absolute accuracy on MATH Level 5 for Llama3.2-3B), with effective generalization to unseen datasets (+9.4\% absolute on SAT MATH). Furthermore, we benchmark our PRM against existing open-source reward models, demonstrating superior alignment with reasoning quality and more consistent guidance for downstream generation. Our work demonstrates the potential of PRM-guided, step-level GFlowNets for developing more robust and versatile mathematical reasoning in LLMs.

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Adam Younsi, Ahmed Attia, Abdalgader Abubaker, Mohamed El Amine Seddik, Hakim Hacid, Salem Lahlou. 2025-10-13. Accurate and Diverse LLM Mathematical Reasoning via Automated PRM-Guided GFlowNets. https://arxiv.org/abs/2504.19981

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