SAU: Smooth Activation Function Using Convolution with Approximate Identities

Koushik Biswas, Sandeep Kumar, Shilpak Banerjee, Ashish Kumar Pandey

Abstract: Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.63%, 2.95%, and 2.50% improvement with ShuffleNet V2 (2.0x), PreActResNet 50 and ResNet 50 models respectively on the CIFAR100 dataset and 2.31% improvement with ShuffleNet V2 (1.0x) model on ImageNet-1k dataset.