Title: IOT: Instance-wise Layer Reordering for Transformer Structures. Abstract: With sequentially stacked self-attention, (optional) encoder-decoder attention, and feed-forward layers, Transformer achieves big success in natural language processing (NLP), and many variants have been proposed. Currently, almost all these models assume that the \emph{layer order} is fixed and kept the same across data samples. We observe that different data samples actually favor different orders of the layers. Based on this observation, in this work, we break the assumption of the fixed layer order in Transformer and introduce instance-wise layer reordering into model structure. Our Instance-wise Ordered Transformer (IOT) can model variant functions by reordered layers, which enables each sample to select the better one to improve the model performance under the constraint of almost same number of parameters. To achieve this, we introduce a light predictor with negligible parameter and inference cost to decide the most capable and favorable layer order for any input sequence. Experiments on $3$ tasks (neural machine translation, abstractive summarization, and code generation) and $9$ datasets demonstrate consistent improvements of our method. We further show that our method can also be applied to other architectures beyond Transformer. Our code is released at Github\footnote{\url{https://github.com/instance-wise-ordered-transformer/IOT}}.