From the perspective of the layer normalization (LN) positions, the architectures of Transformers can be categorized into two types: Post-LN and Pre-LN. Recent Transformers tend to be Pre-LN because, in Post-LN with deep Transformers (e.g., those with ten or more layers), the training is often unstable, resulting in useless models. However, Post-LN has consistently achieved better performance than Pre-LN in relatively shallow Transformers (e.g., those with six or fewer layers). This study first investigates the reason for these discrepant observations empirically and theoretically and made the following discoveries: 1, the LN in Post-LN is the main source of the vanishing gradient problem that leads to unstable training, whereas Pre-LN prevents it, and 2, Post-LN tends to preserve larger gradient norms in higher layers during the back-propagation, which may lead to effective training. Exploiting the new findings, we propose a method that can provide both high stability and effective training by a simple modification of Post-LN. We conduct experiments on a wide range of text generation tasks. The experimental results demonstrate that our method outperforms Pre-LN, and enables stable training regardless of the shallow or deep layer settings. Our code is publicly available at https://github.com/takase/b2t_connection.

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.