  Cross-lingual or cross-domain correspondences play key roles in tasks ranging
from machine translation to transfer learning. Recently, purely unsupervised
methods operating on monolingual embeddings have become effective alignment
tools. Current state-of-the-art methods, however, involve multiple steps,
including heuristic post-hoc refinement strategies. In this paper, we cast the
correspondence problem directly as an optimal transport (OT) problem, building
on the idea that word embeddings arise from metric recovery algorithms. Indeed,
we exploit the Gromov-Wasserstein distance that measures how similarities
between pairs of words relate across languages. We show that our OT objective
can be estimated efficiently, requires little or no tuning, and results in
performance comparable with the state-of-the-art in various unsupervised word
translation tasks.
