Large language models (LLMs) struggle with cross-lingual knowledge transfer: they sometimes hallucinate when asked in one language about facts expressed in a different language during training. This work introduces a controlled setting to study the causes and training dynamics of this phenomenon by training small Transformer models from scratch on synthetic multilingual datasets. Depending on (1) the correlation between facts and the language they were learned in (informativeness), and (2) the ease of language identification (extractability), models either develop unified representations across languages or separate representations; only when representations are unified do facts transfer across languages. Based on these insights, we propose a unifying perspective which explains a range of prior observations concerning cross-lingual transfer in multilingual LLMs. Our work shows controlled settings can shed light on pre-training dynamics and suggests methods to encourage representational unification as part of training that would improve LLMs' cross-lingual transfer.

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