Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

Recent research in neural machine translation has explored flexible generation orders, as an alternative to left-to-right generation. However, training non-monotonic models brings a new complication: how to search for a good ordering when there is a combinatorial explosion of orderings arriving at the same final result? Also, how do these automatic orderings compare with the actual behaviour of human translators? Current models rely on manually built biases or are left to explore all possibilities on their own. In this paper, we analyze the orderings produced by human post-editors and use them to train an automatic post-editing system. We compare the resulting system with those trained with left-to-right and random post-editing orderings. We observe that humans tend to follow a nearly left-to-right order, but with interesting deviations, such as preferring to start by correcting punctuation or verbs.