SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions
For researchers in neural network design, SechKAN offers a new KAN architecture that improves performance over existing KANs and MLPs on standard benchmarks, but the improvement is incremental.
SechKAN introduces a Kolmogorov-Arnold Network variant using hyperbolic secant basis functions, achieving superior performance over MLPs and other KAN variants on function fitting, PDEs, and image classification (MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100) with comparable parameter counts, though with slightly longer runtime than MLPs.
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.