In this paper, we turn our attention to the interworking between the activation functions and the batch normalization, which is a virtually mandatory technique to train deep networks currently. We propose the activation function Displaced Rectifier Linear Unit (DReLU) by conjecturing that extending the identity function of ReLU to the third quadrant enhances compatibility with batch normalization. Moreover, we used statistical tests to compare the impact of using distinct activation functions (ReLU, LReLU, PReLU, ELU, and DReLU) on the learning speed and test accuracy performance of standardized VGG and Residual Networks state-of-the-art models. These convolutional neural networks were trained on CIFAR-100 and CIFAR-10, the most commonly used deep learning computer vision datasets. The results showed DReLU speeded up learning in all models and datasets. Besides, statistical significant performance assessments (p<0.05) showed DReLU enhanced the test accuracy presented by ReLU in all scenarios. Furthermore, DReLU showed better test accuracy than any other tested activation function in all experiments with one exception, in which case it presented the second best performance. Therefore, this work demonstrates that it is possible to increase performance replacing ReLU by an enhanced activation function.
A new activation function called Displaced Rectifier Linear Unit is proposed. It is showed to enhance the training and inference performance of batch normalized convolutional neural networks. The paper compares and suggests against the usage of batch normalization after using rectifier linear units This paper proposes an activation function, called displaced ReLU, to improve the performance of CNNs that use batch normalization.