We investigate the behavior of maps learned by machine translation methods. The maps translate words by projecting between word embedding spaces of different languages. We locally approximate these maps using linear maps, and find that they vary across the word embedding space. This demonstrates that the underlying maps are non-linear. Importantly, we show that the locally linear maps vary by an amount that is tightly correlated with the distance between the neighborhoods on which they are trained. Our results can be used to test non-linear methods, and to drive the design of more accurate maps for word translation.

Leveraging zero-shot learning to learn mapping functions between vector spaces of different languages is a promising approach to bilingual dictionary induction. However, methods using this approach have not yet achieved high accuracy on the task. In this paper, we propose a bridging approach, where our main contribution is a knowledge distillation training objective. As teachers, rich resource translation paths are exploited in this role. And as learners, translation paths involving low resource languages learn from the teachers. Our training objective allows seamless addition of teacher translation paths for any given low resource pair. Since our approach relies on the quality of monolingual word embeddings, we also propose to enhance vector representations of both the source and target language with linguistic information. Our experiments on various languages show large performance gains from our distillation training objective, obtaining as high as 17% accuracy improvements.