Natural-Logarithm-Rectified Activation Function in Convolutional Neural Networks
Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on ReLU have been proposed, but each carry performance drawbacks. In this paper, we propose an improved activation function, which we name the natural-logarithm-rectified linear unit (NLReLU). NLReLU uses the parametric natural logarithmic transform to improve ReLU, and is defined as $f(x)=\ln (\beta \cdot \max (0,x)+1.0)$. NLReLU not only retains the sparse activation characteristic of ReLU, but it also alleviates the “dying $\mathrm {R}\mathrm {e}\mathrm {L}\mathrm {U}$” and vanishing gradient problems to some extent. It also reduces the bias shift effect and heteroscedasticity of neuron data distributions among network layers in order to accelerate the learning process. The proposed method was verified across ten convolutional neural networks with different depths for two essential datasets. Experiments illustrate that convolutional neural networks with NLReLU exhibit higher accuracy than those with ReLU, and that NLReLU is comparable to other well-known activation functions. NLReLU provides 0.16% and 2.04% higher classification accuracy on average compared to ReLU when used in shallow convolutional neural networks with the MNIST and CIFAR-10 datasets, respectively. The average accuracy of deep convolutional neural networks with NLReLU is 1.35% higher on average with the CIFAR-10 dataset.