  The ability to extract high-quality translation dictionaries from monolingual
word embedding spaces depends critically on the geometric similarity of the
spaces -- their degree of "isomorphism." We address the root-cause of faulty
cross-lingual mapping: that word embedding training resulted in the underlying
spaces being non-isomorphic. We incorporate global measures of isomorphism
directly into the Skip-gram loss function, successfully increasing the relative
isomorphism of trained word embedding spaces and improving their ability to be
mapped to a shared cross-lingual space. The result is improved bilingual
lexicon induction in general data conditions, under domain mismatch, and with
training algorithm dissimilarities. We release IsoVec at
https://github.com/kellymarchisio/isovec.
