Don't fear peculiar activation functions: EUAF and beyond

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR-10, Tiny-ImageNet, and ImageNet. The models utilizing PEUAF achieve the best performance across several baseline industrial datasets. Specifically, in image datasets, the models that incorporate mixed activation functions (with PEUAF) exhibit competitive test accuracy despite the low accuracy of models with only PEUAF. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.