  Back-translation - data augmentation by translating target monolingual data -
is a crucial component in modern neural machine translation (NMT). In this
work, we reformulate back-translation in the scope of cross-entropy
optimization of an NMT model, clarifying its underlying mathematical
assumptions and approximations beyond its heuristic usage. Our formulation
covers broader synthetic data generation schemes, including sampling from a
target-to-source NMT model. With this formulation, we point out fundamental
problems of the sampling-based approaches and propose to remedy them by (i)
disabling label smoothing for the target-to-source model and (ii) sampling from
a restricted search space. Our statements are investigated on the WMT 2018
German - English news translation task.
