Are All Good Word Vector Spaces Isomorphic?

Existing algorithms for aligning cross-lingual word vector spaces assume that vector spaces are approximately isomorphic. As a result, they perform poorly or fail completely on non-isomorphic spaces. Such non-isomorphism has been hypothesised to result almost exclusively from typological differences between languages. In this work, we ask whether non-isomorphism is also crucially a sign of degenerate word vector spaces. We present a series of experiments across diverse languages which show that, besides inherent typological differences, variance in performance across language pairs can largely be attributed to the size of the monolingual resources available, and to the properties and duration of monolingual training (e.g. "under-training").

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