SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions

AI 中文解读

SechKAN来了！一种新型神经网络架构，用一个像钟形曲线一样的数学函数代替传统方法，在保持模型“身材”不变的情况下，性能却比经典网络和其他同类架构更出色。通俗地说，现在的神经网络就像一座大楼，需要各种“房间”来接受信息、处理问题。KAN是一种更聪明的房间设计方式，而SechKAN则用了一种叫“双曲正割”的特殊曲线，这种曲线形状平滑、反应集中、梯度稳定，让网络学习起来更靠谱。同时，团队通过巧妙的参数压缩，让SechKAN的模型大小和传统多层感知机差不多，但功能更强大。实验显示，在数字识别、衣物分类、物体识别等标准数据集上，SechKAN的表现全面领先，尤其在函数拟合和偏微分方程求解这类科学计算任务上优势明显。虽然它的运行速度比传统网络稍慢一点，但已经比其它KAN变体快了不少。这项技术的意义在于，它可能让未来的AI更聪明、更稳健，尤其是在需要高精度图像识别或科学仿真计算的场景——比如手机拍照识别植物、自动驾驶中的行人检测、气象预测模型等，都能用更小的算力成本获得更好的结果，让AI在更多领域“靠谱”起来。

arXiv:2607.18290v1 Announce Type: new Abstract: In recent years, Kolmogorov-Arnold Networks (KANs) have attracted increasing attention due to their effectiveness in machine learning and scientific computing tasks, offering a new paradigm for neural network design. In this paper, we present SechKAN, a KAN architecture based on hyperbolic secant (sech) functions. The hyperbolic secant basis is used for its smooth bell-shaped form, localized responses, and stable gradients. We employ 1D linear transformations to reduce the number of parameters, allowing SechKAN to remain comparable to multilayer perceptrons (MLPs) in model size. Experimental results indicate the effectiveness of SechKAN in function fitting, PDE problems, and image classification tasks on benchmark datasets, including MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. SechKAN achieves superior performance compared to MLPs and other KAN variants while maintaining a similar number of parameters. However, its running time, while better than that of other KAN variants, is slightly longer than that of MLPs.