Linear embedding transformation has been shown to be effective for zero-shot cross-lingual transfer tasks and achieve surprisingly promising results. However, cross-lingual embedding space mapping is usually studied in static word-level embeddings, where a space transformation is derived by aligning representations of translation pairs that are referred from dictionaries. We move further from this line and investigate a contextual embedding alignment approach which is sense-level and dictionary-free. To enhance the quality of the mapping, we also provide a deep view of properties of contextual embeddings, i.e., anisotropy problem and its solution. Experiments on zero-shot dependency parsing through the concept-shared space built by our embedding transformation substantially outperform state-of-the-art methods using multilingual embeddings.
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