  Large language models respond well in high-resource languages like English
but struggle in low-resource languages. It may arise from the lack of
high-quality instruction following data in these languages. Directly
translating English samples into these languages can be a solution but
unreliable, leading to responses with translation errors and lacking
language-specific or cultural knowledge. To address this issue, we propose a
novel method to construct cross-lingual instruction following samples with
instruction in English and response in low-resource languages. Specifically,
the language model first learns to generate appropriate English instructions
according to the natural web texts in other languages as responses. The
candidate cross-lingual instruction tuning samples are further refined and
diversified. We have employed this method to build a large-scale cross-lingual
instruction tuning dataset on 10 languages, namely X-Instruction. The
instruction data built using our method incorporate more language-specific
knowledge compared with the naive translation method. Experimental results have
shown that the response quality of the model tuned on X-Instruction greatly
exceeds the model distilled from a powerful teacher model, reaching or even
surpassing the ones of ChatGPT. In addition, we find that models tuned on
cross-lingual instruction following samples can follow the instruction in the
output language without further tuning.
