FC-KAN：Kolmogorov-Arnold网络中的函数组合
FC-KAN: Function Combinations in Kolmogorov-Arnold Networks
AI总结：
本文提出FC-KAN，通过元素级运算结合B-spline、小波和径向基函数等数学函数，改进KAN网络，实验表明其在MNIST和Fashion-MNIST数据集上优于其他模型。
摘要：
本文介绍FC-KAN，一种利用元素级运算结合B-spline、小波和径向基函数等数学函数的Kolmogorov-Arnold网络。我们探讨了多种组合方法，包括求和、元素级乘积、求和与元素级乘积之和、二次和三次函数表示、拼接、拼接输出的线性变换等。在实验中，我们比较了FC-KAN与多层感知机网络（MLP）及其他现有KANs，如BSRBF-KAN、EfficientKAN、FastKAN和FasterKAN，在MNIST和Fashion-MNIST数据集上的性能。两种FC-KAN变体，分别使用B-spline和导数高斯（DoG）以及B-spline和二次函数形式的线性变换输出，平均5次独立训练运行中优于其他模型。我们期望FC-KAN能通过函数组合设计未来的KANs。我们的仓库在：https://github.com/hoangthangta/FC_KAN。
英文摘要：
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 Derivative 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
