However, they still rely on one critical assumption which leads them to degraded performance for distant language pairs: they assume approximate isomorphism (Barone, 2016; between monolingual embedding spaces to learn the initial seed dictionary.
they assume very similar geometric constellations between two monolingual spaces: due to the Zipfian phenomena in language (Zipf, 1949) such near-isomorphism can be satisfied only for similar languages and for similar domains used for training monolingual vectors.