提出新型柯西激活函数，构建高效神经网络XNet用于高维问题求解
Cauchy activation function and XNet
- 基于复分析柯西积分定理设计新激活函数
- 在图像分类与偏微分方程求解上超越经典模型
- 适合需要高精度的科学计算与复杂模式识别任务
我们提出一种新的激活函数——柯西激活函数，该函数源自复分析中的柯西积分定理，专为高精度问题设计。由此衍生出一类新型神经网络，称为（完）XNet（简称XNet）。实验表明，XNet在图像分类任务中显著优于MNIST和CIFAR-10等基准模型，在求解低维与高维偏微分方程（PDEs）方面也大幅超越物理信息神经网络（PINNs）。该方法特别适用于高维、高精度建模场景。
原文摘要 · Abstract (English)
We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This innovation has led to the creation of a new class of neural networks, which we call (Comple)XNet, or simply XNet. We will demonstrate that XNet is particularly effective for high-dimensional challenges such as image classification and solving Partial Differential Equations (PDEs). Our evaluations show that XNet significantly outperforms established benchmarks like MNIST and CIFAR-10 in computer vision, and offers substantial advantages over Physics-Informed Neural Networks (PINNs) in both low-dimensional and high-dimensional PDE scenarios.
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