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.
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