Skip connection, is a widely-used technique to improve the performance and the convergence of deep neural networks, which is believed to relieve the difficulty in optimization due to non-linearity by propagating a linear component through the neural network layers. However, from another point of view, it can also be seen as a modulating mechanism between the input and the output, with the input scaled by a pre-defined value one. In this work, we investigate how the scale factors in the effectiveness of the skip connection and reveal that a trivial adjustment of the scale will lead to spurious gradient exploding or vanishing in line with the deepness of the models, which could be addressed by normalization, in particular, layer normalization, which induces consistent improvements over the plain skip connection. Inspired by the findings, we further propose to adaptively adjust the scale of the input by recursively applying skip connection with layer normalization, which promotes the performance substantially and generalizes well across diverse tasks including both machine translation and image classification datasets.
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