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We propose a novel geometric approach for learning bilingual mappings given monolingual embeddings and a bilingual dictionary. Our approach decouples learning the transformation from the source language to the target language into (a) learning rotations for language-specific embeddings to align them to a common space, and (b) learning a similarity metric in the common space to model similarities between the embeddings. We model the bilingual mapping problem as an optimization problem on smooth<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.08773v3">arXiv:1808.08773v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tkic4ej7drbc3glenbnop6wkja">fatcat:tkic4ej7drbc3glenbnop6wkja</a> </span>
more »... iemannian manifolds. We show that our approach outperforms previous approaches on the bilingual lexicon induction and cross-lingual word similarity tasks. We also generalize our framework to represent multiple languages in a common latent space. In particular, the latent space representations for several languages are learned jointly, given bilingual dictionaries for multiple language pairs. We illustrate the effectiveness of joint learning for multiple languages in zero-shot word translation setting. Our implementation is available at https://github.com/anoopkunchukuttan/geomm .
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