  Existing sentence ordering approaches generally employ encoder-decoder
frameworks with the pointer net to recover the coherence by recurrently
predicting each sentence step-by-step. Such an autoregressive manner only
leverages unilateral dependencies during decoding and cannot fully explore the
semantic dependency between sentences for ordering. To overcome these
limitations, in this paper, we propose a novel Non-Autoregressive Ordering
Network, dubbed \textit{NAON}, which explores bilateral dependencies between
sentences and predicts the sentence for each position in parallel. We claim
that the non-autoregressive manner is not just applicable but also particularly
suitable to the sentence ordering task because of two peculiar characteristics
of the task: 1) each generation target is in deterministic length, and 2) the
sentences and positions should match exclusively. Furthermore, to address the
repetition issue of the naive non-autoregressive Transformer, we introduce an
exclusive loss to constrain the exclusiveness between positions and sentences.
To verify the effectiveness of the proposed model, we conduct extensive
experiments on several common-used datasets and the experimental results show
that our method outperforms all the autoregressive approaches and yields
competitive performance compared with the state-of-the-arts. The codes are
available at:
\url{https://github.com/steven640pixel/nonautoregressive-sentence-ordering}.
