Journal of Data Science and Modeling

A parametric activation function based on Wendland RBF

Articles in Press

Document Type : Research Manuscript

Author

Majid Darehmiraki

Department of mathematics, Behbahan Khatam Alanbi University of Technology

10.22054/jdsm.2026.89529.1083
Abstract
This paper introduces a novel parametric activation function based on Wendland radial basis functions (RBFs) for deep neural networks. Wendland RBFs, known for their compact support, smoothness, and positive definiteness in approximation theory, are adapted to address limitations of traditional activation functions like ReLU, sigmoid, and tanh. The proposed enhanced Wendland activation combines a standard Wendland component with linear and exponential terms, offering tunable locality, improved gradient propagation, and enhanced stability during training. Theoretical analysis rigorously examines derivative behavior, smoothness, gradient flow, and saturation properties, demonstrating advantages over ReLU, GELU, and Swish including strictly positive gradients, $C^2$-continuity, near-unity gradient decay, and well-conditioned Jacobians. Empirical experiments on synthetic tasks and benchmark datasets confirm competitive performance, with comprehensive diagnostic analyses validating the theoretical claims. Results show that the Wendland-based activation achieves superior accuracy in certain scenarios, particularly in regression tasks, while maintaining computational efficiency. The study bridges classical RBF theory with modern deep learning, suggesting that Wendland activations can mitigate overfitting and improve generalization through localized, smooth transformations.

Keywords

Activation function
Deep learning
Wendland RBF
Compact support
Parametric
Subjects
Journal of Data Science and Modeling

Articles in Press, Accepted Manuscript
Available Online from 31 August 2026

Home

Guide for Authors

Submit Manuscript

Contact Us