FC-KAN: Function Combinations in Kolmogorov-Arnold Networks

• Main Authors: Ta, Hoang-Thang, Thai, Duy-Quy, Rahman, Abu Bakar Siddiqur, Sidorov, Grigori, Gelbukh, Alexander
• Format: Journal Article
• Language: English
• Published: 03.09.2024
• Subjects: Computer Science - Computation and Language; Computer Science - Learning
• DOI: 10.48550/arxiv.2409.01763

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.