Title: Iterative Decoding for Compositional Generalization in Transformers. Abstract: Deep learning models do well at generalizing to in-distribution data but struggle to generalize compositionally, i.e., to combine a set of learned primitives to solve more complex tasks. In particular, in sequence-to-sequence (seq2seq) learning, transformers are often unable to predict even marginally longer examples than those seen during training. This paper introduces iterative decoding, an alternative to seq2seq learning that (i) improves transformer compositional generalization and (ii) evidences that, in general, seq2seq transformers do not learn iterations that are not unrolled. Inspired by the idea of compositionality---that complex tasks can be solved by composing basic primitives---training examples are broken down into a sequence of intermediate steps that the transformer then learns iteratively. At inference time, the intermediate outputs are fed back to the transformer as intermediate inputs until an end-of-iteration token is predicted. Through numerical experiments, we show that transfomers trained via iterative decoding outperform their seq2seq counterparts on the PCFG dataset, and solve the problem of calculating Cartesian products between vectors longer than those seen during training with 100% accuracy, a task at which seq2seq models have been shown to fail. We also illustrate a limitation of iterative decoding, specifically, that it can make sorting harder to learn on the CFQ dataset.