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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Veröffentlicht in:Neural networks Jg. 188; S. 107375
Hauptverfasser: Li, Xin, Xia, Zhihong, Zhang, Hongkun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Elsevier Ltd 01.08.2025
Schlagworte:
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-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2025.107375