Randomly translational activation inspired by the input distributions of ReLU

Deep convolutional neural networks have achieved great success on many visual tasks (e.g., image classification). Non-linear activation plays a very important role in deep convolutional neural networks (CNN). It is found that the input distribution of non-linear activation is like Gaussian distribution and the most of the inputs are concentrated near zero. It makes the learned CNN likely sensitive to the small jitter of the non-linear activation input. Meanwhile, CNN is easily prone to overfitting with deep architecture. To solve the above problems, we make full use of the input distributions of non-linear activation and propose the randomly translational non-linear activation for deep CNN. In the training stage, non-linear activation function is randomly translated by an offset sampled from Gaussian distribution. In the test stage, the non-linear activation with zero offset is used. Based on our proposed method, the input distribution of non-linear activation is relatively scattered. As the result, the learned CNN is robust to the small jitter of the non-linear activation input. Our proposed method can be also seen as the regularization of non-linear activation to reduce overfitting. Compared to the original non-linear activation, our proposed method can improve classification accuracy without increasing computation cost. Experimental results on CIFAR-10/CIFAR-100, SVHN, and ImageNet demonstrate the effectiveness of the proposed method. For example, the reductions of error rates with VGG architecture on CIFAR-10/CIFAR-100 are 0.55% and 1.61%, respectively. Even when the noise is added to the input image, our proposed method still has much better classification accuracy on CIFAR-10/CIFAR-100.