发表机构
University of Information Technology; Vietnam National University（信息技术大学; 越南国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究提出基于双曲正割函数的SechKAN架构，利用双曲正割基及一维线性变换减少参数，在函数拟合、PDE问题和图像分类任务中表现出色，相比MLP和其他KAN变体性能更优，虽运行时间稍长但仍有优势。
AI 中文摘要
近年来，柯尔莫哥洛夫 - 阿诺德网络（KANs）因其在机器学习和科学计算任务中的有效性而备受关注，为神经网络设计提供了新范式。本文提出了基于双曲正割（sech）函数的KAN架构SechKAN。使用双曲正割基是因其平滑钟形、局部响应和稳定梯度。采用一维线性变换减少参数数量，使SechKAN在模型规模上与多层感知器（MLP）相当。实验结果表明SechKAN在基准数据集上的函数拟合、偏微分方程问题和图像分类任务中有效，与MLP和其他KAN变体相比，参数数量相近时性能更优，不过运行时间比MLP稍长。
英文摘要
In recent years KolmogorovArnold Networks KANs have attracted increasing attention due to their effectiveness in machine learning and scientific computing offering a new paradigm for neural network design In this paper we present SechKAN a novel KAN based on hyperbolic secant sech functions The hyperbolic secant basis is adopted for its smooth bellshaped form localized responses and wellbehaved gradients We employ a 1D linear projection to reduce the number of parameters allowing SechKAN to maintain a model size comparable to that of multilayer perceptrons MLPs Experimental results show the effectiveness of SechKAN on function fitting PDE surrogate modeling and image classification benchmarks including MNIST FashionMNIST CIFAR10 and CIFAR100 On function fitting SechKAN achieves performance comparable to both MLPs and representative KAN variants On PDE surrogate modeling it outperforms MLPs and achieves competitive or better performance than representative KAN variants On image classification benchmarks SechKAN achieves the best performance among the evaluated KAN variants while remaining competitive with MLPs using a comparable number of parameters However SechKAN still incurs higher computational cost than MLPs and some KAN variants Our source code is publicly available at https://github.com/hoangthangta/All-KAN.
Comments37 pages
