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The performance of neural machine translation systems is commonly evaluatedin terms of BLEU. However, due to its reliance on target language propertiesand generation, the BLEU metric does not allow an assessment of whichtranslation directions are more difficult to model. In this paper, we proposecross-mutual information (XMI): an asymmetric information-theoretic metric ofmachine translation difficulty that exploits the probabilistic nature of mostneural machine translation models. XMI allows us to better evaluate thedifficulty of translating text into the target language while controlling forthe difficulty of the target-side generation component independent of thetranslation task. We then present the first systematic and controlled study ofcross-lingual translation difficulties using modern neural translation systems.Code for replicating our experiments is available online athttps://github.com/e-bug/nmt-difficulty.

It's Easier to Translate out of English than into it: Measuring Neural Translation Difficulty by Cross-Mutual Information