For years, many neural networks have been developed based on the Kolmogorov-Arnold Representation Theorem (KART), which was created to address Hilbert's 13th problem. Recently, relying on KART, Kolmogorov-Arnold Networks (KANs) have attracted attention from the research community, stimulating the use of polynomial functions such as B-splines and RBFs. However, these functions are not fully supported by GPU devices and are still considered less popular. In this paper, we propose the use of fast computational functions, such as ReLU and trigonometric functions (e.g., ReLU, sin, cos, arctan), as basis components in Kolmogorov-Arnold Networks (KANs). By integrating these function combinations into the network structure, we aim to enhance computational efficiency. Experimental results show that these combinations maintain competitive performance while offering potential improvements in training time and generalization.

In this paper, we introduce FC-KAN, a Kolmogorov-Arnold Network (KAN) that leverages combinations of popular mathematical functions such as B-splines, wavelets, and radial basis functions on low-dimensional data through element-wise operations. We explore several methods for combining the outputs of these functions, including sum, element-wise product, the addition of sum and element-wise product, quadratic function representation, and concatenation. In our experiments, we compare FC-KAN with multi-layer perceptron network (MLP) and other existing KANs, such as BSRBF-KAN, EfficientKAN, FastKAN, and FasterKAN, on the MNIST and Fashion-MNIST datasets. A variant of FC-KAN, which uses a combination of outputs from B-splines and Difference of Gaussians (DoG) in the form of a quadratic function, outperformed all other models on the average of 5 independent training runs. We expect that FC-KAN can leverage function combinations to design future KANs. Our repository is publicly available at: https://github.com/hoangthangta/FC_KAN.