  In this work, we present an empirical study of generation order for machine
translation. Building on recent advances in insertion-based modeling, we first
introduce a soft order-reward framework that enables us to train models to
follow arbitrary oracle generation policies. We then make use of this framework
to explore a large variety of generation orders, including uninformed orders,
location-based orders, frequency-based orders, content-based orders, and
model-based orders. Curiously, we find that for the WMT'14 English $\to$ German
translation task, order does not have a substantial impact on output quality,
with unintuitive orderings such as alphabetical and shortest-first matching the
performance of a standard Transformer. This demonstrates that traditional
left-to-right generation is not strictly necessary to achieve high performance.
On the other hand, results on the WMT'18 English $\to$ Chinese task tend to
vary more widely, suggesting that translation for less well-aligned language
pairs may be more sensitive to generation order.
