  Cross-lingual word embeddings can be applied to several natural language
processing applications across multiple languages. Unlike prior works that use
word embeddings based on the Euclidean space, this short paper presents a
simple and effective cross-lingual Word2Vec model that adapts to the Poincar\'e
ball model of hyperbolic space to learn unsupervised cross-lingual word
representations from a German-English parallel corpus. It has been shown that
hyperbolic embeddings can capture and preserve hierarchical relationships. We
evaluate the model on both hypernymy and analogy tasks. The proposed model
achieves comparable performance with the vanilla Word2Vec model on the
cross-lingual analogy task, the hypernymy task shows that the cross-lingual
Poincar\'e Word2Vec model can capture latent hierarchical structure from free
text across languages, which are absent from the Euclidean-based Word2Vec
representations. Our results show that by preserving the latent hierarchical
information, hyperbolic spaces can offer better representations for
cross-lingual embeddings.
