  Neural translation models have proven to be effective in capturing sufficient
information from a source sentence and generating a high-quality target
sentence. However, it is not easy to get the best effect for bidirectional
translation, i.e., both source-to-target and target-to-source translation using
a single model. If we exclude some pioneering attempts, such as multilingual
systems, all other bidirectional translation approaches are required to train
two individual models. This paper proposes to build a single end-to-end
bidirectional translation model using a two-dimensional grid, where the
left-to-right decoding generates source-to-target, and the bottom-to-up
decoding creates target-to-source output. Instead of training two models
independently, our approach encourages a single network to jointly learn to
translate in both directions. Experiments on the WMT 2018
German$\leftrightarrow$English and Turkish$\leftrightarrow$English translation
tasks show that the proposed model is capable of generating a good translation
quality and has sufficient potential to direct the research.
