Cross-lingual word embeddings are becoming increasingly important in multilingual NLP. Recently, it has been shown that these embeddings can be effectively learned by aligning two disjoint monolingual vector spaces through linear transformations, using no more than a small bilingual dictionary as supervision. In this work, we propose to apply an additional transformation after the initial alignment step, which moves cross-lingual synonyms towards a middle point between them. By applying this transformation our aim is to obtain a better cross-lingual integration of the vector spaces. In addition, and perhaps surprisingly, the monolingual spaces also improve by this transformation. This is in contrast to the original alignment, which is typically learned such that the structure of the monolingual spaces is preserved. Our experiments confirm that the resulting cross-lingual embeddings outperform state-of-the-art models in both monolingual and cross-lingual evaluation tasks.
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