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

The Secret is in the Spectra: Predicting Cross-lingual Task Performance with Spectral Similarity Measures