  The many-to-many multilingual neural machine translation can translate
between language pairs unseen during training, i.e., zero-shot translation.
Improving zero-shot translation requires the model to learn universal
representations and cross-mapping relationships to transfer the knowledge
learned on the supervised directions to the zero-shot directions. In this work,
we propose the state mover's distance based on the optimal theory to model the
difference of the representations output by the encoder. Then, we bridge the
gap between the semantic-equivalent representations of different languages at
the token level by minimizing the proposed distance to learn universal
representations. Besides, we propose an agreement-based training scheme, which
can help the model make consistent predictions based on the semantic-equivalent
sentences to learn universal cross-mapping relationships for all translation
directions. The experimental results on diverse multilingual datasets show that
our method can improve consistently compared with the baseline system and other
contrast methods. The analysis proves that our method can better align the
semantic space and improve the prediction consistency.
