Stacking non-linear layers allows deep neural networks to model complicated functions, and including residual connections in Transformer layers is beneficial for convergence and performance. However, residual connections may make the model "forget" distant layers and fail to fuse information from previous layers effectively. Selectively managing the representation aggregation of Transformer layers may lead to better performance. In this paper, we present a Transformer with depth-wise LSTMs connecting cascading Transformer layers and sub-layers. We show that layer normalization and feed-forward computation within a Transformer layer can be absorbed into depth-wise LSTMs connecting pure Transformer attention layers. Our experiments with the 6-layer Transformer show significant BLEU improvements in both WMT 14 English-German / French tasks and the OPUS-100 many-to-many multilingual NMT task, and our deep Transformer experiments demonstrate the effectiveness of depth-wise LSTM on the convergence and performance of deep Transformers.

The choice of hyper-parameters affects the performance of neural models. While much previous research (Sutskever et al., 2013; Duchi et al., 2011; Kingma and Ba, 2015) focuses on accelerating convergence and reducing the effects of the learning rate, comparatively few papers concentrate on the effect of batch size. In this paper, we analyze how increasing batch size affects gradient direction, and propose to evaluate the stability of gradients with their angle change. Based on our observations, the angle change of gradient direction first tends to stabilize (i.e. gradually decrease) while accumulating mini-batches, and then starts to fluctuate. We propose to automatically and dynamically determine batch sizes by accumulating gradients of mini-batches and performing an optimization step at just the time when the direction of gradients starts to fluctuate. To improve the efficiency of our approach for large models, we propose a sampling approach to select gradients of parameters sensitive to the batch size. Our approach dynamically determines proper and efficient batch sizes during training. In our experiments on the WMT 14 English to German and English to French tasks, our approach improves the Transformer with a fixed 25k batch size by +0.73 and +0.82 BLEU respectively.