  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 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 variance in performance across language pairs is not only due
to typological differences, but can mostly be attributed to the size of the
monolingual resources available, and to the properties and duration of
monolingual training (e.g. "under-training").
