Revisiting the linearity in cross-lingual embedding mappings: from a perspective of word analogies

Most cross-lingual embedding mapping algorithms assume the optimised transformation functions to be linear. Recent studies showed that on some occasions, learning a linear mapping does not work, indicating that the commonly-used assumption may fail. However, it still remains unclear under which conditions the linearity of cross-lingual embedding mappings holds. In this paper, we rigorously explain that the linearity assumption relies on the consistency of analogical relations encoded by multilingual embeddings. We did extensive experiments to validate this claim. Empirical results based on the analogy completion benchmark and the BLI task demonstrate a strong correlation between whether mappings capture analogical information and are linear.