  Cross-lingual word vectors are typically obtained by fitting an orthogonal
matrix that maps the entries of a bilingual dictionary from a source to a
target vector space. Word vectors, however, are most commonly used for sentence
or document-level representations that are calculated as the weighted average
of word embeddings. In this paper, we propose an alternative to word-level
mapping that better reflects sentence-level cross-lingual similarity. We
incorporate context in the transformation matrix by directly mapping the
averaged embeddings of aligned sentences in a parallel corpus. We also
implement cross-lingual mapping of deep contextualized word embeddings using
parallel sentences with word alignments. In our experiments, both approaches
resulted in cross-lingual sentence embeddings that outperformed
context-independent word mapping in sentence translation retrieval.
Furthermore, the sentence-level transformation could be used for word-level
mapping without loss in word translation quality.
