Large language models (LLMs) demonstrate exceptional performance on complex reasoning tasks. However, despite their strong reasoning capabilities in high-resource languages (e.g., English and Chinese), a significant performance gap persists in other languages. To investigate this gap in Korean, we introduce HRM8K, a benchmark comprising 8,011 English-Korean parallel bilingual math problems. Through systematic analysis of model behaviors, we identify a key finding: these performance disparities stem primarily from difficulties in comprehending non-English inputs, rather than limitations in reasoning capabilities. Based on these findings, we propose UST (Understand, Solve, and Translate), a method that strategically uses English as an anchor for reasoning and solution generation. By fine-tuning the model on 130k synthetically generated data points, UST achieves a 10.91% improvement on the HRM8K benchmark and reduces the multilingual performance gap from 11.6% to 0.7%. Additionally, we show that improvements from UST generalize effectively to different Korean domains, demonstrating that capabilities acquired from machine-verifiable content can be generalized to other areas. We publicly release the benchmark, training dataset, and models.

本研究针对语言模型在非高资源语言（如韩语）上的推理性能差距，提出了HRM8K基准测试。通过分析，我们发现此差距主要源于模型对非英语输入的理解困难，而非推理能力的限制。基于此，提出UST方法，通过在英文基础上进行推理和解决，显著提升了模型表现，并有效减少了多语言的性能差距。

理解、解决与翻译：弥合多语言数学推理差距