Duy-Quy Thai

Hoang-Thang Ta, Duy-Quy Thai, Abu Bakar Siddiqur Rahman et al.

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, representations of quadratic and cubic functions, concatenation, linear transformation of the concatenated output, and others. In our experiments, we compare FC-KAN with a multi-layer perceptron network (MLP) and other existing KANs, such as BSRBF-KAN, EfficientKAN, FastKAN, and FasterKAN, on the MNIST and Fashion-MNIST datasets. Two variants of FC-KAN, which use a combination of outputs from B-splines and Difference of Gaussians (DoG) and from B-splines and linear transformations in the form of a quadratic function, outperformed overall 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.

Hoang-Thang Ta, Duy-Quy Thai, Anh Tran et al.

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 drive groundbreaking research and enable transformative applications across various scientific domains involving neural networks. However, existing KANs often require significantly more parameters in their network layers than MLPs. To address this limitation, this paper introduces PRKANs (Parameter-Reduced Kolmogorov-Arnold Networks), 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 outperform several existing KANs, and their variant with attention mechanisms rivals 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: https://github.com/hoangthangta/All-KAN.

Hoang-Thang Ta, Duy-Quy Thai, Phuong-Linh Tran-Thi

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.