Cauchy activation function and XNet
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910802065227776 |
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| author | Li, Xin Xia, Zhihong Zhang, Hongkun |
| author_facet | Li, Xin Xia, Zhihong Zhang, Hongkun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cauchy activation function and XNet Li, Xin Xia, Zhihong Zhang, Hongkun Machine Learning Computer Vision and Pattern Recognition Neural and Evolutionary Computing 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. |
| title | Cauchy activation function and XNet |
| topic | Machine Learning Computer Vision and Pattern Recognition Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2409.19221 |