相关论文: Enhancing Neural Function Approximation: The XNet …

This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These neural networks are simple because they are designed with a…

Classical results in neural network approximation theory show how arbitrary continuous functions can be approximated by networks with a single hidden layer, under mild assumptions on the activation function. However, the classical theory…

In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) activation without the curse of dimensionality. In other…

Deep learning has long been dominated by multi-layer perceptrons (MLPs), which have demonstrated superiority over other optimizable models in various domains. Recently, a new alternative to MLPs has emerged - Kolmogorov-Arnold Networks…

This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…

We firstly simulated disease dynamics by KAN (Kolmogorov-Arnold Networks) nearly 4 years ago, but the kernel functions in the edge include the exponential number of infected and discharged people and is also in line with the…

Multilayer Perceptron (MLP), as a simple yet powerful model, continues to be widely used in classification and regression tasks. However, traditional MLPs often struggle to efficiently capture nonlinear relationships in load data when…

The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks…

We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…

Machine-learning architectures, such as Convolutional Neural Networks (CNNs) are vulnerable to adversarial attacks: inputs crafted carefully to force the system output to a wrong label. Since machine-learning is being deployed in…

In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…

We introduce a method to train Quantized Neural Networks (QNNs) --- neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At train-time the quantized weights and activations are used for computing…

Activation functions play a decisive role in determining the capacity of Deep Neural Networks as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions…

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…

Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning models (PIKANs) and deep operator models (DeepOKANs) for solving…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

Kolmogorov-Arnold Networks (KANs) have very recently been introduced into the world of machine learning, quickly capturing the attention of the entire community. However, KANs have mostly been tested for approximating complex functions or…

We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts and can be easily adapted to partial convexity. We give an universal approximation theorem in the full…

Binarized neural networks (BNNs) have shown exciting potential for utilising neural networks in embedded implementations where area, energy and latency constraints are paramount. With BNNs, multiply-accumulate (MAC) operations can be…

Despite their immense success, deep convolutional neural networks (CNNs) can be difficult to optimize and costly to train due to hundreds of layers within the network depth. Conventional convolutional operations are fundamentally limited by…