Reasoning capabilities of large language models are primarily studied for English, even when pretrained models are multilingual. In this work, we investigate to what extent English reasoning finetuning with long chain-of-thoughts (CoTs) can generalize across languages. First, we find that scaling up inference compute for English-centric reasoning language models (RLMs) improves multilingual mathematical reasoning across many languages including low-resource languages, to an extent where they outperform models twice their size. Second, we reveal that while English-centric RLM's CoTs are naturally predominantly English, they consistently follow a quote-and-think pattern to reason about quoted non-English inputs. Third, we discover an effective strategy to control the language of long CoT reasoning, and we observe that models reason better and more efficiently in high-resource languages. Finally, we observe poor out-of-domain reasoning generalization, in particular from STEM to cultural commonsense knowledge, even for English. Overall, we demonstrate the potentials, study the mechanisms and outline the limitations of crosslingual generalization of English reasoning test-time scaling. We conclude that practitioners should let English-centric RLMs reason in high-resource languages, while further work is needed to improve reasoning in low-resource languages and out-of-domain contexts.

本研究解决了大语言模型在多语言推理能力上的研究空白，尤其是英语推理模型在训练后如何在其他语言上表现。通过扩展推理计算，发现英语推理模型可以在多种语言中实现跨语言数学推理的提升，尤其是在高资源语言中更为有效。这项研究揭示了跨语言推理的潜力和机制，同时指出了低资源语言和不同领域知识推理的局限性。

通过测试时扩展进行跨语言推理