ProbAct: A Probabilistic Activation Function for Deep Neural Networks

Activation functions play an important role in the training of artificial neural networks and the Rectified Linear Unit (ReLU) has been the mainstream in recent years. Most of the activation functions currently used are deterministic in nature, whose input-output relationship is fixed. In this work, we propose a probabilistic activation function, called ProbAct. The output value of ProbAct is sampled from a normal distribution, with the mean value same as the output of ReLU and with a fixed or trainable variance for each element. In the trainable ProbAct, the variance of the activation distribution is trained through back-propagation. We also show that the stochastic perturbation through ProbAct is a viable generalization technique that can prevent overfitting. In our experiments, we demonstrate that when using ProbAct, it is possible to boost the image classification performance on CIFAR-10, CIFAR-100, and STL-10 datasets.