Title: On Layer Normalization in the Transformer Architecture. Abstract: The Transformer architecture is popularly used in natural language processing tasks. To train a Transformer model, a carefully designed learning rate warm-up stage is usually needed: the learning rate has to be set to an extremely small value at the beginning of the optimization and then gradually increases in some given number of iterations. Such a stage is shown to be crucial to the final performance and brings more hyper-parameter tunings. In this paper, we study why the learning rate warm-up stage is important in training the Transformer and theoretically show that the location of layer normalization matters. It can be proved that at the beginning of the optimization, for the original Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Then using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful to avoid this problem. Such an analysis motivates us to investigate a slightly modified Transformer architecture which locates the layer normalization inside the residual blocks. We show that the gradients in this Transformer architecture are well-behaved at initialization. Given these findings,  we are the first to show that this Transformer variant is easier and faster to train. The learning rate warm-up stage can be safely removed, and the training time can be largely reduced on a wide range of applications.