An activation function is a crucial component of a neural network that introduces non-linearity in the network. The state-of-the-art performance of a neural network depends also on the perfect choice of an activation function. We propose two novel non-monotonic smooth trainable activation functions, called ErfAct and Pserf. Experiments suggest that the proposed functions improve the network performance significantly compared to the widely used activations like ReLU, Swish, and Mish. Replacing ReLU by ErfAct and Pserf, we have 5.68% and 5.42% improvement for top-1 accuracy on Shufflenet V2 (2.0x) network in CIFAR100 dataset, 2.11% and 1.96% improvement for top-1 accuracy on Shufflenet V2 (2.0x) network in CIFAR10 dataset, 1.0%, and 1.0% improvement on mean average precision (mAP) on SSD300 model in Pascal VOC dataset.

Deep learning researchers have a keen interest in proposing new novel activation functions that can boost neural network performance. A good choice of activation function can have a significant effect on improving network performance and training dynamics. Rectified Linear Unit (ReLU) is a popular hand-designed activation function and is the most common choice in the deep learning community due to its simplicity though ReLU has some drawbacks. In this paper, we have proposed two new novel activation functions based on approximation of the maximum function, and we call these functions Smooth Maximum Unit (SMU and SMU-1). We show that SMU and SMU-1 can smoothly approximate ReLU, Leaky ReLU, or more general Maxout family, and GELU is a particular case of SMU. Replacing ReLU by SMU, Top-1 classification accuracy improves by 6.22%, 3.39%, 3.51%, and 3.08% on the CIFAR100 dataset with ShuffleNet V2, PreActResNet-50, ResNet-50, and SeNet-50 models respectively. Also, our experimental evaluation shows that SMU and SMU-1 improve network performance in a variety of deep learning tasks like image classification, object detection, semantic segmentation, and machine translation compared to widely used activation functions.