A Periodic Mapping Activation Function: Mathematical Properties and Application in Convolutional Neural Networks

Xu Chen, Yinlei Cheng, Siqin Wang, Guangliang Sang (), Ken Nah and Jianmin Wang
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Xu Chen: College of Design and Innovation, Tongji University, Shanghai 200092, China
Yinlei Cheng: School of Artificial Intelligence and Innovative Design, Beijing Institute of Fashion Technology, Beijing 100029, China
Siqin Wang: International Design Trend Center, Hongik University, Seoul 04068, Republic of Korea
Guangliang Sang: International Design Trend Center, Hongik University, Seoul 04068, Republic of Korea
Ken Nah: International Design Trend Center, Hongik University, Seoul 04068, Republic of Korea
Jianmin Wang: College of Design and Innovation, Tongji University, Shanghai 200092, China

Mathematics, 2025, vol. 13, issue 17, 1-22

Abstract: Activation functions play a crucial role in ensuring training stability, convergence speed, and overall performance in both convolutional and attention-based networks. In this study, we introduce two novel activation functions, each incorporating a sine component and a constraint term. To assess their effectiveness, we replace the activation functions in four representative architectures—VGG16, ResNet50, DenseNet121, and Vision Transformers—covering a spectrum from lightweight to high-capacity models. We conduct extensive evaluations on four benchmark datasets (CIFAR-10, CIFAR-100, MNIST, and Fashion-MNIST), comparing our methods against seven widely used activation functions. The results consistently demonstrate that our proposed functions achieve superior performance across all tested models and datasets. From a design application perspective, the proposed functional periodic structure also facilitates rich and structurally stable activation visualizations, enabling designers to trace model attention, detect surface biases early, and make informed aesthetic or accessibility decisions during interface prototyping.

Keywords: activation function; convolutional neural networks; vision transformers; benchmark datasets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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