Related papers: Continuous approximation by convolutional neural n…
Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…
The Convolutional Neural Network (CNN) is one of the most prominent neural network architectures in deep learning. Despite its widespread adoption, our understanding of its universal approximation properties has been limited due to its…
Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult…
We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer…
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In this paper, we establish a connection between both network…
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…
We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our…
The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can…
We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of TNs for functions from classical smoothness classes?'' and…
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…
Currently, increasingly deeper neural networks have been applied to improve their accuracy. In contrast, We propose a novel wider Convolutional Neural Networks (CNN) architecture, motivated by the Multi-column Deep Neural Networks and the…
Convolutional Neural Networks (CNNs) are powerful models that achieve impressive results for image classification. In addition, pre-trained CNNs are also useful for other computer vision tasks as generic feature extractors. This paper aims…
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on…
We consider whether deep convolutional networks (CNNs) can represent decision functions with similar accuracy as recurrent networks such as LSTMs. First, we show that a deep CNN with an architecture inspired by the models recently…
Convolutional neural networks (CNN) are built upon the classical McCulloch-Pitts neuron model, which is essentially a linear model, where the nonlinearity is provided by a separate activation function. Several researchers have proposed…
Convolutional neural networks (CNNs) have shown great success in computer vision, approaching human-level performance when trained for specific tasks via application-specific loss functions. In this paper, we propose a method for augmenting…
In this work we describe a Convolutional Neural Network (CNN) to accurately predict the scene illumination. Taking image patches as input, the CNN works in the spatial domain without using hand-crafted features that are employed by most…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…