SechKAN: New Kolmogorov-Arnold Network Variant for Enhanced Performance

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional neural networks, offering a new design paradigm. This research presents SechKAN, an innovative KAN architecture that leverages hyperbolic secant (sech) functions. The choice of hyperbolic secant is based on its smooth, bell-shaped form, localized responses, and stable gradients, which contribute to its effectiveness. To keep the model size comparable to standard multilayer perceptrons (MLPs), SechKAN incorporates 1D linear transformations, efficiently reducing the number of parameters. This design allows it to achieve high performance without significantly increasing computational overhead in terms of model size. Experimental evaluations demonstrate SechKAN's superior capabilities in diverse applications, including function fitting, solving partial differential equations (PDEs), and image classification on benchmark datasets like MNIST and CIFAR. While its running time is slightly longer than MLPs, it outperforms other KAN variants in speed and achieves better accuracy than both MLPs and existing KANs with a similar parameter count.