用可学习三角函数构建单参数化神经网络，提升精度与速度
LArctan-SKAN: Simple and Efficient Single-Parameterized Kolmogorov-Arnold Networks using Learnable Trigonometric Function
- 用可学习三角函数构造单参数化函数，简化模型结构
- 在MNIST上准确率超越所有对比模型，训练速度提升超49%
- 适合追求高效高精度的深度学习研究者使用
本文提出一种新方法，通过基于三角函数构建的单参数化函数（SFunc），设计单参数化柯尔莫戈罗夫-阿诺德网络（SKAN）。开发了三种新变体：LSin-SKAN、LCos-SKAN和LArctan-SKAN。在MNIST数据集上的实验表明，LArctan-SKAN在准确率和计算效率方面均表现优异。其测试集准确率显著优于所有纯KAN模型，包括FourierKAN、LSS-SKAN和Spl-KAN，也超过混合MLP模型如MLP+rKAN和MLP+fKAN。同时，其训练速度分别比MLP+rKAN和MLP+fKAN提升535.01%和49.55%。结果验证了基于三角函数的SKAN的有效性与潜力。代码已公开于https://github.com/chikkkit/LArctan-SKAN。
原文摘要 · Abstract (English)
This paper proposes a novel approach for designing Single-Parameterized Kolmogorov-Arnold Networks (SKAN) by utilizing a Single-Parameterized Function (SFunc) constructed from trigonometric functions. Three new SKAN variants are developed: LSin-SKAN, LCos-SKAN, and LArctan-SKAN. Experimental validation on the MNIST dataset demonstrates that LArctan-SKAN excels in both accuracy and computational efficiency. Specifically, LArctan-SKAN significantly improves test set accuracy over existing models, outperforming all pure KAN variants compared, including FourierKAN, LSS-SKAN, and Spl-KAN. It also surpasses mixed MLP-based models such as MLP+rKAN and MLP+fKAN in accuracy. Furthermore, LArctan-SKAN exhibits remarkable computational efficiency, with a training speed increase of 535.01% and 49.55% compared to MLP+rKAN and MLP+fKAN, respectively. These results confirm the effectiveness and potential of SKANs constructed with trigonometric functions. The experiment code is available at https://github.com/chikkkit/LArctan-SKAN .
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