Cauchy activation function and XNet

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 netw...

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Bibliographic Details
Published in:Neural networks Vol. 188; p. 107375
Main Authors: Li, Xin, Xia, Zhihong, Zhang, Hongkun
Format: Journal Article
Language:English
Published: United States Elsevier Ltd 01.08.2025
Subjects:
Algorithms
Cauchy Integral Theorem
Humans
Image classification
Neural Networks, Computer
Physics-Informed Neural Networks
Physics-Informed Neural Networks
Cauchy Integral Theorem
Image classification
ISSN:0893-6080, 1879-2782, 1879-2782
Online Access:Get full text
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Summary: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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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2025.107375