Recent advances have enabled Large Language Models (LLMs) to tackle reasoning tasks by generating chain-of-thought (CoT) rationales, yet these gains have largely applied to high-resource languages, leaving low-resource languages behind. In this work, we first investigate CoT techniques in extremely low-resource scenarios through previous prompting, model-editing, and fine-tuning approaches. We introduce English-Pivoted CoT Training, leveraging the insight that LLMs internally operate in a latent space aligned toward the dominant language. Given input in a low-resource language, we perform supervised fine-tuning to generate CoT in English and output the final response in the target language. Across mathematical reasoning benchmarks, our approach outperforms other baselines with up to 28.33% improvement in low-resource scenarios. Our analysis and additional experiments, including Mixed-Language CoT and Two-Stage Training, show that explicitly separating language understanding from reasoning enhances cross-lingual reasoning abilities. To facilitate future work, we also release \emph{LC2024}, the first benchmark for mathematical tasks in Irish, an extremely low-resource and endangered language. Our results and resources highlight a practical pathway to multilingual reasoning without extensive retraining in every extremely low-resource language, despite data scarcity.

翻译：近期进展使得大语言模型（LLMs）能够通过生成思维链（CoT）推理过程来处理推理任务，但这些成果主要应用于高资源语言，低资源语言仍被忽视。本研究首先通过先前的提示、模型编辑与微调方法，探究了极低资源场景下的CoT技术。我们提出了以英语为枢纽的CoT训练方法，其基于LLMs在内部运作于一个向主导语言对齐的隐空间的洞见。给定低资源语言的输入，我们通过监督微调生成英语的CoT，并以目标语言输出最终回答。在数学推理基准测试中，我们的方法在低资源场景下优于其他基线，最高提升达28.33%。我们的分析及包括混合语言CoT与两阶段训练在内的补充实验表明，显式地将语言理解与推理分离能够增强跨语言推理能力。为促进未来研究，我们还发布了首个针对极低资源与濒危语言——爱尔兰语的数学任务基准测试集\\emph{LC2024}。我们的成果与资源为在数据稀缺条件下，无需对每种极低资源语言进行大规模重新训练即可实现多语言推理，指明了一条实用路径。