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arXiv 2512.19093cs.AI

工具增强的混合集成推理与蒸馏用于双语数学问题求解

Tool-Augmented Hybrid Ensemble Reasoning with Distillation for Bilingual Mathematical Problem Solving

Boston University(波士顿大学);University of Pennsylvania(宾夕法尼亚大学);Northwestern University(西北大学);University of Illinois Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校)

Peiqing Lu, Yuan Zhang, Haoyun Zhang, Jiasen Zheng, Kejian Tong, Wenjun Wu

AI总结:

HERALD通过结合自适应学习、工具强化学习和知识蒸馏,提升双语数学问题求解的准确性和稳定性。

摘要:

双语数学问题求解需要语言推理与符号计算之间有清晰的联系。大语言模型通常在处理语言方面表现良好,但在准确计算方面较弱。本文提出了HERALD(混合集成推理与自适应学习和蒸馏)框架,该框架利用NuminaMath-7B-TIR、GPT-4o和Mistral-7B结合推理与计算。HERALD使用自适应路由、基于工具的强化学习和知识蒸馏来连接不同的推理路径。置信度校准保持权重稳定,双路径检查保持结果正确。强化学习控制工具使用以减少冗余,蒸馏降低延迟而不损害准确性。系统表明,结合符号检查、自适应集成和双语微调有助于实现流畅的推理和精确的计算。HERALD为多语言数学推理提供了实用的解决方案,具有更好的准确性、稳定性和清晰度。

英文摘要:

Bilingual mathematical problem solving needs a clear link between language reasoning and symbolic calculation. Large language models often handle language well but are weak in accurate computation. This paper presents HERALD (Hybrid Ensemble Reasoning with Adaptive Learning and Distillation), a framework that joins reasoning and calculation using NuminaMath-7B-TIR, GPT-4o, and Mistral-7B. HERALD uses adaptive routing, tool-based reinforcement learning, and knowledge distillation to connect different reasoning paths. Confidence calibration keeps weighting stable, and dual-path checking keeps results correct. Reinforcement learning controls tool use to cut redundancy, and distillation lowers delay without hurting accuracy. The system shows that combining symbolic checking, adaptive ensembles, and bilingual fine-tuning helps achieve both fluent reasoning and precise calculation. HERALD offers a practical solution for multilingual mathematical reasoning with better accuracy, stability, and clarity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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