相关论文: Universal Approximation Properties for an ODENet a…

We introduce the unbounded depth neural network (UDN), an infinitely deep probabilistic model that adapts its complexity to the training data. The UDN contains an infinite sequence of hidden layers and places an unbounded prior on a…

The paper discusses the use of the Absolute activation function in classification neural networks. An examples are shown of using this activation function in simple and more complex problems. Using as a baseline LeNet-5 network for solving…

This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…

The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks. However, the critical width enabling the universal approximation has not been…

The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters are appropriately chosen real numbers. This paper examines the…

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…

We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations…

There exists many resource allocation problems in the field of wireless communications which can be formulated as the generalized assignment problems (GAP). GAP is a generic form of linear sum assignment problem (LSAP) and is more…

This paper focuses on establishing $L^2$ approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based on a decomposition theorem for convolutional kernels with a large spatial…

Deep neural networks (DNN) have achieved great success in image restoration. However, most DNN methods are designed as a black box, lacking transparency and interpretability. Although some methods are proposed to combine traditional…

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Deep learning has shown strong potential for scientific discovery, but its ability to model macroscopic rigid-body kinematic constraints remains underexplored. We study this problem on spatial over-constrained mechanisms and propose…

Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…

Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

We propose o1Neuro, a new neural network model built on sparse indicator activation neurons, with two key statistical properties. (1) Constructive universal approximation: At the population level, a deep o1Neuro can approximate any…

Grasp synthesis is one of the challenging tasks for any robot object manipulation task. In this paper, we present a new deep learning-based grasp synthesis approach for 3D objects. In particular, we propose an end-to-end 3D Convolutional…

We present a new framework of applying deep neural networks (DNN) to devise a universal discrete denoiser. Unlike other approaches that utilize supervised learning for denoising, we do not require any additional training data. In such…

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

Deep residual networks (ResNets) made a recent breakthrough in deep learning. The core idea of ResNets is to have shortcut connections between layers that allow the network to be much deeper while still being easy to optimize avoiding…