相关论文: Quantitative approximation results for complex-val…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

In this paper, we have extended the well-established universal approximator theory to neural networks that use the unbounded ReLU activation function and a nonlinear softmax output layer. We have proved that a sufficiently large neural…

This study explores the number of neurons required for a Rectified Linear Unit (ReLU) neural network to approximate multivariate monomials. We establish an exponential lower bound on the complexity of any shallow network approximating the…

Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on…

This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectively neural networks…

Neural networks with ReLU activation function have been shown to be universal function approximators and learn function mapping as non-smooth functions. Recently, there is considerable interest in the use of neural networks in applications…

Recent deep neural network-based device classification studies show that complex-valued neural networks (CVNNs) yield higher classification accuracy than real-valued neural networks (RVNNs). Although this improvement is (intuitively)…

The study of the expressive power of neural networks has investigated the fundamental limits of neural networks. Most existing results assume real-valued inputs and parameters as well as exact operations during the evaluation of neural…

We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functions $\varrho:\mathbb{C}\to \mathbb{C}$ that have the property…

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Solutions of evolution equation generally lies in certain Bochner-Sobolev spaces, in which the solution may has regularity and integrability properties for the time variable that can be different for the space variables. Therefore, in this…

We study approximation limits of single-hidden-layer neural networks with analytic activation functions under global coefficient constraints. Under uniform $\ell^1$ bounds, or more generally sub-exponential growth of the coefficients, we…

Many real-world signal sources are complex-valued, having real and imaginary components. However, the vast majority of existing deep learning platforms and network architectures do not support the use of complex-valued data. MRI data is…

Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…

Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most…

Traditional Convolutional Neural Networks (CNNs) typically use the same activation function (usually ReLU) for all neurons with non-linear mapping operations. For example, the deep convolutional architecture Inception-v4 uses ReLU. To…

The expressive power of neural networks is important for understanding deep learning. Most existing works consider this problem from the view of the depth of a network. In this paper, we study how width affects the expressiveness of neural…

The purpose of the present paper is to study the computation complexity of deep ReLU neural networks to approximate functions in H\"older-Nikol'skii spaces of mixed smoothness $H_\infty^\alpha(\mathbb{I}^d)$ on the unit cube…

The choice of activation function fundamentally shapes the representational capacity and parameter efficiency of deep neural networks, yet most widely used activations lack rigorous theoretical guarantees on these properties. We provide a…