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.

翻译：本文提出FC-KAN，一种Kolmogorov-Arnold网络（KAN），其通过对低维数据进行逐元素运算，融合了B样条、小波与径向基函数等常用数学函数的组合。我们探索了多种组合这些函数输出的方法，包括求和、逐元素乘积、求和与逐元素乘积的叠加、二次与三次函数的表示、拼接、对拼接输出的线性变换以及其他方式。实验中，我们在MNIST与Fashion-MNIST数据集上，将FC-KAN与多层感知机网络（MLP）及其他现有KAN模型（如BSRBF-KAN、EfficientKAN、FastKAN与FasterKAN）进行了比较。FC-KAN的两种变体——分别采用B样条与高斯差分（DoG）的组合输出，以及采用B样条与以二次函数形式呈现的线性变换的组合输出——在5次独立训练的平均性能上超越了所有其他模型。我们预期FC-KAN能够借助函数组合为未来KAN的设计提供支持。代码仓库已公开于：https://github.com/hoangthangta/FC_KAN。