SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions

2026-06-30

AI Summary

This work addresses the performance and efficiency limitations of existing Kolmogorov–Arnold Networks (KANs) by proposing SechKAN, a novel KAN architecture based on the hyperbolic secant (sech) activation function. SechKAN introduces, for the first time, the smooth, locally responsive, and well-behaved sech basis functions into the KAN framework, combined with one-dimensional linear projections to control parameter count. This design achieves significantly enhanced representational capacity over multilayer perceptrons (MLPs) while maintaining comparable model size. Empirical evaluations demonstrate that SechKAN consistently outperforms both state-of-the-art KAN variants and MLPs across diverse tasks, including function approximation, surrogate modeling of partial differential equations, and image classification on MNIST, Fashion-MNIST, and CIFAR benchmarks, confirming its effectiveness and strong generalization capability, despite room for further computational optimization.

Abstract

In recent years, Kolmogorov-Arnold Networks (KANs) have attracted increasing attention due to their effectiveness in machine learning and scientific computing tasks, offering a new paradigm for neural network design. In this paper, we present SechKAN, a KAN architecture based on hyperbolic secant (sech) functions. The hyperbolic secant basis is used for its smooth bell-shaped form, localized responses, and stable gradients. We employ 1D linear transformations to reduce the number of parameters, allowing SechKAN to remain comparable to multilayer perceptrons (MLPs) in model size. Experimental results indicate the effectiveness of SechKAN in function fitting, PDE problems, and image classification tasks on benchmark datasets, including MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. SechKAN achieves superior performance compared to MLPs and other KAN variants while maintaining a similar number of parameters. However, its running time, while better than that of other KAN variants, is slightly longer than that of MLPs.

Problem

• Kolmogorov-Arnold Networks
• hyperbolic secant functions
• computational cost
• model efficiency
• neural network design

Innovation

• Kolmogorov-Arnold Networks
• hyperbolic secant function
• parameter efficiency
• PDE surrogate modeling
• function approximation