  Multi-source translation is an approach to exploit multiple inputs (e.g. in
two different languages) to increase translation accuracy. In this paper, we
examine approaches for multi-source neural machine translation (NMT) using an
incomplete multilingual corpus in which some translations are missing. In
practice, many multilingual corpora are not complete due to the difficulty to
provide translations in all of the relevant languages (for example, in TED
talks, most English talks only have subtitles for a small portion of the
languages that TED supports). Existing studies on multi-source translation did
not explicitly handle such situations. This study focuses on the use of
incomplete multilingual corpora in multi-encoder NMT and mixture of NMT experts
and examines a very simple implementation where missing source translations are
replaced by a special symbol <NULL>. These methods allow us to use incomplete
corpora both at training time and test time. In experiments with real
incomplete multilingual corpora of TED Talks, the multi-source NMT with the
<NULL> tokens achieved higher translation accuracies measured by BLEU than
those by any one-to-one NMT systems.
