Related papers: Enhancing Neural Function Approximation: The XNet …

In this paper we present a class of convolutional neural networks (CNNs) called non-overlapping CNNs in the study of approximation capabilities of CNNs. We prove that such networks with sigmoidal activation function are capable of…

In this work we propose CVKAN, a complex-valued Kolmogorov-Arnold Network (KAN), to join the intrinsic interpretability of KANs and the advantages of Complex-Valued Neural Networks (CVNNs). We show how to transfer a KAN and the necessary…

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 Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation…

The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that…

This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approximation within weighted $C^k$-spaces and weighted Sobolev…

Deep net architectures have constantly evolved over the past few years, leading to significant advancements in a wide array of computer vision tasks. However, besides high accuracy, many applications also require a low computational load…

Neural architecture search (NAS) automates the design process of high-performing architectures, but remains bottlenecked by expensive performance evaluation. Most existing studies that achieve faster evaluation are mostly tied to cell-based…

Nowadays, the rapid growth of Deep Neural Network (DNN) architectures has established them as the defacto approach for providing advanced Machine Learning tasks with excellent accuracy. Targeting low-power DNN computing, this paper examines…

Previous works proved that the combination of the linear neuron network with nonlinear activation functions (e.g. ReLu) can achieve nonlinear function approximation. However, simply widening or deepening the network structure will introduce…

Convolution and self-attention are acting as two fundamental building blocks in deep neural networks, where the former extracts local image features in a linear way while the latter non-locally encodes high-order contextual relationships.…

A new network with super approximation power is introduced. This network is built with Floor ($\lfloor x\rfloor$) or ReLU ($\max\{0,x\}$) activation function in each neuron and hence we call such networks Floor-ReLU networks. For any…

Recently, the authors of \cite{SYZ22} developed a neural network with width $36d(2d + 1)$ and depth $11$, which utilizes a special activation function called the elementary universal activation function, to achieve the super approximation…

Learned activation functions in models like Kolmogorov-Arnold Networks (KANs) outperform fixed-activation architectures in terms of accuracy and interpretability; however, their computational complexity poses critical challenges for…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

In this article, we prove approximation theorems in classes of deep and shallow neural networks with analytic activation functions by elementary arguments. We prove for both real and complex networks with non-polynomial activation that the…

The success of Neural networks in providing miraculous results when applied to a wide variety of tasks is astonishing. Insight in the working can be obtained by studying the universal approximation property of neural networks. It is proved…

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…

Kolmogorov-Arnold Network (KAN) has attracted growing interest for its strong function approximation capability. In our previous work, KAN and its variants were explored in score regression for blind image quality assessment (BIQA).…

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…