English(EN) Counterexample Generation via Per-Theorem Symbolic Verifiers: When Imitation Hurts and Reinforcement Repairs

新数据集SymCE训练LLM生成数学反例

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-05 04:00

研究人员开发了SymCE，这是一个新的数据集和训练环境，旨在提高大型语言模型生成数学定理反例的能力。该方法使用逐定理符号验证器作为奖励函数，解决了模型能够解决正向问题但无法证伪相关错误陈述的已知局限性。使用SymCE和强化学习（特别是GRPO）进行训练表明，虽然单独的监督微调会降低模型在正确定理上的性能，但强化学习能有效修复这一点并增强反例生成能力。 AI

影响这项研究可能带来更强大的LLM数学推理能力，提高它们识别和纠正形式化证明和问题解决中错误的能力。

排序理由该集群包含一篇学术论文，详细介绍了LLM的新数据集和训练方法。[lever_c_demoted from research: ic=1 ai=1.0]

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报道来源 [1]

arXiv cs.AI TIER_1 English(EN) · Omar Farouk Zouak, Houssam Eddine Boukhalfa, Soumaya Lakehal, Shiv Katiyar, Samia Nefti-Meziani · 2026-10-05 04:00

通过按定理符号验证器生成反例：模仿何时有害，强化何时修复

arXiv:2610.02444v1 Announce Type: cross Abstract: Large language models often solve a theorem forward yet fail to disprove a closely related false one: a falsification gap that supervised fine-tuning does not close and can actively worsen. We frame counterexample generation as co…

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通过按定理符号验证器生成反例：模仿何时有害，强化何时修复

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