Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectified linear activation unit (SReLU) to learn both convex and non-convex functions, imitating the multiple function forms given by the two fundamental laws, namely the Webner-Fechner law and the Stevens law, in psychophysics and neural sciences. Specifically, SReLU consists of three piecewise linear functions, which are formulated by four learnable parameters. The SReLU is learned jointly with the training of the whole deep network through back propagation. During the training phase, to initialize SReLU in different layers, we propose a "freezing" method to degenerate SReLU into a predefined leaky rectified linear unit in the initial several training epochs and then adaptively learn the good initial values. SReLU can be universally used in the existing deep networks with negligible additional parameters and computation cost. Experiments with two popular CNN architectures, Network in Network and GoogLeNet on scale-various benchmarks including CI-FAR10, CIFAR100, MNIST and ImageNet demonstrate that SReLU achieves remarkable improvement compared to other activation functions.
We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5 and 17.0 , respectively, which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overfitting in the fully connected layers we employed a recently developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3 , compared to 26.2 achieved by the second-best entry.