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. Since we represent the rotated embeddings in a common latent space, our approach can easily represent multiple languages in a common space. We also show that these multilingual embeddings can be learned jointly given bilingual dictionaries for multiple language pairs. We demonstrate the effectiveness of the multilingual embeddings in one zero-shot word translation setting: word translation using these multilingual embeddings is better than word translation using a pivot language when no source-target bilingual dictionary is available, but source-pivot and pivot-target bilingual dictionaries are available.

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。

在潜藏度量空间中学习多语言词向量：一种几何方法