  Cross-lingual word embeddings aim to bridge the gap between high-resource and
low-resource languages by allowing to learn multilingual word representations
even without using any direct bilingual signal. The lion's share of the methods
are projection-based approaches that map pre-trained embeddings into a shared
latent space. These methods are mostly based on the orthogonal transformation,
which assumes language vector spaces to be isomorphic. However, this criterion
does not necessarily hold, especially for morphologically-rich languages. In
this paper, we propose a self-supervised method to refine the alignment of
unsupervised bilingual word embeddings. The proposed model moves vectors of
words and their corresponding translations closer to each other as well as
enforces length- and center-invariance, thus allowing to better align
cross-lingual embeddings. The experimental results demonstrate the
effectiveness of our approach, as in most cases it outperforms state-of-the-art
methods in a bilingual lexicon induction task.
