Training Instability and Disharmony Between ReLU and Batch Normalization

Deep neural networks based on batch normalization and ReLU-like activation functions experience instability during early stages of training owing to the high gradient induced by temporal gradient explosion. ReLU reduces the variance by more than the expected amount and batch normalization amplifies the gradient during its recovery. In this paper, we explain the explosion of a gradient mathematically while the forward propagation remains stable, and also the alleviation of the problem during training. Based on this, we propose a Layer-wise Asymmetric Learning rate Clipping (LALC) algorithm, which outperforms existing learning rate scaling methods in large batch training and can also be used to replace WarmUp in small batch training.