mlsanityData to 7 Oct 2026

Cauchy activation function and XNet

arXiv 2409.19221 ↗First posted 28 Sep 2024cs.LG cs.CV cs.NEcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 20 of its 43 references that are in the map. First posted on arXiv 28 Sep 2024.

Builds on

20 of 43 references.

References · 20

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  4. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  5. 2017Self-Normalizing Neural Networkscited by 591
  6. 2016Error bounds for approximations with deep ReLU networkscited by 567
  7. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  8. 2020Visual Transformers: Token-based Image Representation and Processing for Computer Visioncited by 333
  9. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  10. 2015Unitary Evolution Recurrent Neural Networkscited by 291
  11. 2017Deep Complex Networkscited by 215
  12. 2021Activation Functions in Deep Learning: A Comprehensive Survey and Benchmarkcited by 153
8 more
  1. 2024FeatUp: A Model-Agnostic Framework for Features at Any Resolutioncited by 114
  2. 2020Rational neural networkscited by 75
  3. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
  4. 2021Deep Reinforcement Learning in Computer Vision: A Comprehensive Surveycited by 42
  5. 2017Neural networks and rational functionscited by 40
  6. 2020Discovering Parametric Activation Functionscited by 21
  7. 2024Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networkscited by 21
  8. 2023Theory and Implementation of Complex-Valued Neural Networkscited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2025Complex Physics-Informed Neural Networkcited by 6
  2. 2024Model Comparisons: XNet Outperforms KANcited by 0
  3. 2025Enhancing Neural Function Approximation: The XNet Outperforming KANcited by 0
  4. 2026LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problemscited by 0