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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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
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Abstract	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.
AbstractList	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. 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.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. 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.
ArticleNumber	107375
Author	Zhang, Hongkun Li, Xin Xia, Zhihong
Author_xml	– sequence: 1 givenname: Xin surname: Li fullname: Li, Xin email: xinli2023@u.northwestern.edu organization: Department of Computer Science, Northwestern University, Evanston, IL, USA – sequence: 2 givenname: Zhihong surname: Xia fullname: Xia, Zhihong email: xia@math.northwestern.edu organization: School of Natural Science, Great Bay University, Guangdong, China – sequence: 3 givenname: Hongkun surname: Zhang fullname: Zhang, Hongkun email: hzhang@umass.edu organization: School of Natural Science, Great Bay University, Guangdong, China
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Cites_doi	10.1016/j.neucom.2022.06.111 10.1007/s12065-024-00908-9 10.1038/s41586-019-1923-7 10.1073/pnas.1718942115 10.1109/ACCESS.2022.3232064 10.1016/j.jcp.2019.109136 10.1038/nature14539 10.1016/j.jcp.2018.10.045 10.4208/cicp.OA-2020-0164 10.1038/s42256-021-00302-5 10.1016/j.dsp.2022.103812 10.1038/s41586-019-0912-1 10.1038/s41586-021-03819-2 10.1016/j.neunet.2017.07.002 10.1109/JAS.2022.105743 10.1038/323533a0 10.1016/j.jcp.2018.08.029 10.1016/j.neunet.2022.01.001
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Keywords	Physics-Informed Neural Networks Cauchy Integral Theorem Image classification
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Snippet	We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex...
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SubjectTerms	Algorithms Cauchy Integral Theorem Humans Image classification Neural Networks, Computer Physics-Informed Neural Networks
Title	Cauchy activation function and XNet
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