  Though remarkable successes have been achieved by Neural Machine Translation
(NMT) in recent years, it still suffers from the inadequate-translation
problem. Previous studies show that explicitly modeling the Past and Future
contents of the source sentence is beneficial for translation performance.
However, it is not clear whether the commonly used heuristic objective is good
enough to guide the Past and Future. In this paper, we present a novel dual
framework that leverages both source-to-target and target-to-source NMT models
to provide a more direct and accurate supervision signal for the Past and
Future modules. Experimental results demonstrate that our proposed method
significantly improves the adequacy of NMT predictions and surpasses previous
methods in two well-studied translation tasks.
