The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in the input and the output, compared to the recurrent architectures. We establish connections between the dynamics in Transformer and recurrent networks to argue that several factors including gradient flow along an ensemble of multiple weakly dependent paths play a paramount role in the success of Transformer. We then leverage the dynamics to introduce {\em Multiresolution Transformer Networks} as the first architecture that exploits hierarchical structure in data via self-attention. Our models significantly outperform state-of-the-art recurrent and hierarchical recurrent models on two real-world datasets for query suggestion, namely, \aol and \amazon. In particular, on AOL data, our model registers at least 20\% improvement on each precision score, and over 25\% improvement on the BLEU score with respect to the best performing recurrent model. We thus provide strong evidence that recurrence is not essential for modeling hierarchical structure.
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