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 Riemannian 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
this https URL .

本文提出了一种新的几何方法，通过单语嵌入和双语词典学习双语映射，并将其建模为平滑的黎曼流形上的优化问题，旨在解决双语词典感应和多语言学习中的问题。该方法分解了学习源语言到目标语言的变换，包括学习用于将语言特定的嵌入旋转到公共空间的旋转以及学习在公共空间中对嵌入之间相似性进行建模的相似性度量。结果表明，该方法在双语词典感应和跨语言词相似性任务上优于以前的方法，同时还将该框架推广到了多种语言的共同潜在空间表示上，展示了联合学习处理多语言问题的有效性。