Cauchy activation function and XNet
This addresses the need for more effective neural networks in high-dimensional tasks such as computer vision and PDE solving, though it appears incremental as it builds on existing activation function concepts.
The researchers tackled the problem of high-precision neural network performance by developing the Cauchy activation function based on complex analysis, which led to XNet achieving significant improvements over benchmarks like MNIST and CIFAR-10 in image classification and outperforming PINNs in solving PDEs.
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.