  Recently, convolutional neural networks (CNNs) have been used as a powerful
tool to solve many problems of machine learning and computer vision. In this
paper, we aim to provide insight on the property of convolutional neural
networks, as well as a generic method to improve the performance of many CNN
architectures. Specifically, we first examine existing CNN models and observe
an intriguing property that the filters in the lower layers form pairs (i.e.,
filters with opposite phase). Inspired by our observation, we propose a novel,
simple yet effective activation scheme called concatenated ReLU (CRelu) and
theoretically analyze its reconstruction property in CNNs. We integrate CRelu
into several state-of-the-art CNN architectures and demonstrate improvement in
their recognition performance on CIFAR-10/100 and ImageNet datasets with fewer
trainable parameters. Our results suggest that better understanding of the
properties of CNNs can lead to significant performance improvement with a
simple modification.
