通过函数组合提升Kolmogorov-Arnold网络性能，实测优于主流模型。
FC-KAN: Function Combinations in Kolmogorov-Arnold Networks
- 用B样条、小波等函数组合构建新网络结构
- 在MNIST和Fashion-MNIST上平均表现超越其他KAN与MLP
- 支持多种函数融合方式，适合想改进KAN的研究者
本文提出FC-KAN，一种基于柯尔莫戈洛夫-阿诺德网络（KAN）的新型架构，通过元素级运算组合B样条、小波、径向基函数等常用数学函数处理低维数据。探索了求和、逐元素相乘、加法与乘积结合、二次/三次函数表示、拼接及线性变换等多种组合方式。在MNIST和Fashion-MNIST数据集上的实验表明，两种FC-KAN变体——分别结合B样条与高斯导数（DoG）、B样条与二次函数形式的线性变换——在5次独立训练平均表现上优于MLP及其他现有KAN模型（如BSRBF-KAN、EfficientKAN、FastKAN、FasterKAN）。结果表明函数组合能有效增强KAN表达能力。代码已公开于GitHub。
原文摘要 · Abstract (English)
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.
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