超越输入理解：使用有向无环迹图诊断多语言数学推理
Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs
AI总结：
本文提出有向无环迹图（DATG）框架，通过将推理迹映射到与语言无关的数学锚点和依赖关系，诊断多语言数学推理中的语言影响，并设计Loop-Retry和Formula-Retry两种测试时控制方法改善低资源语言性能。
摘要：
大型推理模型（LRMs）在英语中表现出强大的数学推理能力，但在许多低资源和中资源语言中仍然不太可靠。这种差距通常被解释为无法理解非英语的问题陈述。我们表明这种观点是不完整的：即使问题以英语给出，控制模型的推理语言也会显著降低准确性，这表明语言也影响推理执行本身。为了研究这种效应，我们引入了DATG，一个有向无环迹图框架，将推理迹映射到与语言无关的数学锚点和依赖关系。这使我们能够将目标语言迹与参考DAG对齐，并测量它们是否覆盖所需的数学节点、尊重依赖边以及避免有害的数学动作。在Qwen3系列上跨12种语言的实验表明，非英语推理通常遭受锚点覆盖减少和依赖保真度降低，尤其是在低资源语言中。受此诊断启发，我们提出了Loop-Retry和Formula-Retry，两种针对DATG暴露的失败模式的简单测试时控制方法，并表明它们一致地改善了低资源语言中的目标语言推理性能。
英文摘要：
Large reasoning models (LRMs) achieve strong mathematical reasoning performance in English, but remain much less reliable in many low- and medium-resource languages. This gap is often explained as a failure to understand non-English problem statements. We show that this view is incomplete: even when the problem is given in English, controlling the model's reasoning language can substantially reduce accuracy, suggesting that language also affects reasoning execution itself. To study this effect, we introduce DATG, a Directed Acyclic Trace Graph framework that maps reasoning traces to language-independent mathematical anchors and dependencies. This allows us to align target-language traces with reference DAGs and measure whether they cover required mathematical nodes, respect dependency edges, and avoid harmful mathematical actions. Experiments on the Qwen3 series across 12 languages show that non-English reasoning often suffers from reduced anchor coverage and weaker dependency fidelity, especially in low-resource languages. Motivated by this diagnosis, we propose Loop-Retry and Formula-Retry, two simple test-time controls targeting DATG-exposed failure modes, and show that they consistently improve target-language reasoning performance in low-resource languages.
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。
