Related papers: Enhancing Neural Function Approximation: The XNet …

This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…

Recent developments have introduced Kolmogorov-Arnold Networks (KAN), an innovative architectural paradigm capable of replicating conventional deep neural network (DNN) capabilities while utilizing significantly reduced parameter counts…

This paper presents an experimental study of Kolmogorov-Arnold Networks (KANs) applied to computer vision tasks, particularly image classification. KANs introduce learnable activation functions on edges, offering flexible non-linear…

Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory. In this paper, we aim at constructing deep neural networks (deep nets for short) with three hidden layers to approximate…

Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks. We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to…

We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32x memory saving. In…

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 study 1-bit convolutional neural networks (CNNs), of which both the weights and activations are binary. While efficient, the lacking of representational capability and the training difficulty impede 1-bit CNNs from…

Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based…

Complex-valued neural networks (CVNNs) have been shown to be powerful nonlinear approximators when the input data can be properly modeled in the complex domain. One of the major challenges in scaling up CVNNs in practice is the design of…

Privacy-Preserving Neural Networks (PPNN) are advanced to perform inference without breaching user privacy, which can serve as an essential tool for medical diagnosis to simultaneously achieve big data utility and privacy protection. As one…

Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). However, spline functions may not respect symmetry in tasks,…

We study the approximation properties of shallow neural networks with an activation function which is a power of the rectified linear unit. Specifically, we consider the dependence of the approximation rate on the dimension and the…

Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as an alternative to multilayer perceptrons, suggesting advantages in performance and interpretability. We study a typical binary event classification task in high-energy…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

The Kolmogorov-Arnold Network (KAN) is a new network architecture known for its high accuracy in several tasks such as function fitting and PDE solving. The superior expressive capability of KAN arises from the Kolmogorov-Arnold…

Kolmogorov-Arnold Networks (KANs) have recently emerged as a compelling alternative to multilayer perceptrons, offering enhanced interpretability via functional decomposition. However, existing KAN architectures, including spline-,…

Algorithmic level developments like Convolutional Neural Networks, transformers, attention mechanism, Retrieval Augmented Generation and so on have changed Artificial Intelligence. Recent such development was observed by Kolmogorov-Arnold…