PRKAN: Parameter-Reduced Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks (KANs) represent an innovation in neural network architectures, offering a compelling alternative to Multi-Layer Perceptrons (MLPs) in models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Transformers. By advancing network design, KANs are driving groundbreaking research and enabling transformative applications across various scientific domains involving neural networks. However, existing KANs often require significantly more parameters in their network layers compared to MLPs. To address this limitation, this paper introduces PRKANs (\textbf{P}arameter-\textbf{R}educed \textbf{K}olmogorov-\textbf{A}rnold \textbf{N}etworks), which employ several methods to reduce the parameter count in KAN layers, making them comparable to MLP layers. Experimental results on the MNIST and Fashion-MNIST datasets demonstrate that PRKANs with attention mechanisms outperform several existing KANs and rival the performance of MLPs, albeit with slightly longer training times. Furthermore, the study highlights the advantages of Gaussian Radial Basis Functions (GRBFs) and layer normalization in KAN designs. The repository for this work is available at: \url{https://github.com/hoangthangta/All-KAN}.

FC-KAN: Function Combinations in Kolmogorov-Arnold Networks

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.