Performance in cross-lingual NLP tasks is impacted by the (dis)similarity of
languages at hand: e.g., previous work has suggested there is a connection
between the expected success of bilingual lexicon induction (BLI) and the
assumption of (approximate) isomorphism between monolingual embedding spaces.
In this work we present a large-scale study focused on the correlations between
monolingual embedding space similarity and task performance, covering thousands
of language pairs and four different tasks: BLI, parsing, POS tagging and MT.
We hypothesize that statistics of the spectrum of each monolingual embedding
space indicate how well they can be aligned. We then introduce several
isomorphism measures between two embedding spaces, based on the relevant
statistics of their individual spectra. We empirically show that 1) language
similarity scores derived from such spectral isomorphism measures are strongly
associated with performance observed in different cross-lingual tasks, and 2)
our spectral-based measures consistently outperform previous standard
isomorphism measures, while being computationally more tractable and easier to
interpret. Finally, our measures capture complementary information to
typologically driven language distance measures, and the combination of
measures from the two families yields even higher task performance
correlations.

本研究通过跨语言 NLP 任务探讨了单语嵌入空间的相似性与性能之间的关系，提出了基于光谱的同构测度技术，证明其比先前的标准同构测度方法表现更佳，且其与基于语言距离的方法的结合有助于提高任务性能相关性。