Related papers: Universal Approximation Property of Fully Convolut…
The vulnerability of Convolutional Neural Networks (CNNs) to adversarial samples has recently garnered significant attention in the machine learning community. Furthermore, recent studies have unveiled the existence of universal adversarial…
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network…
Convolutional neural networks (CNNs) have gained widespread usage across various fields such as weather forecasting, computer vision, autonomous driving, and medical image analysis due to its exceptional ability to extract spatial…
Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in…
Deep Convolutional Neural Networks (CNNs) for image classification successively alternate convolutions and downsampling operations, such as pooling layers or strided convolutions, resulting in lower resolution features the deeper the…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…
Convolutional rectifier networks, i.e. convolutional neural networks with rectified linear activation and max or average pooling, are the cornerstone of modern deep learning. However, despite their wide use and success, our theoretical…
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…
In this work we introduce a convolutional neural network (CNN) that jointly handles low-, mid-, and high-level vision tasks in a unified architecture that is trained end-to-end. Such a universal network can act like a `swiss knife' for…
The Convolutional Neural Networks (CNNs), in domains like computer vision, mostly reduced the need for handcrafted features due to its ability to learn the problem-specific features from the raw input data. However, the selection of…
This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D CNNs, comprising multi-channel convolutional layers with…
Deep convolutional neural networks (CNNs) have been shown to perform extremely well at a variety of tasks including subtasks of autonomous driving such as image segmentation and object classification. However, networks designed for these…
Convolutional neural networks (CNN) have become one of the most popular machine learning tools and are being applied in various tasks, however, CNN models are vulnerable to universal perturbations, which are usually human-imperceptible but…
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…
Deep Neural Networks (DNNs) are universal function approximators providing state-of- the-art solutions on wide range of applications. Common perceptual tasks such as speech recognition, image classification, and object tracking are now…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…
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…
Deep Neural networks are efficient and flexible models that perform well for a variety of tasks such as image, speech recognition and natural language understanding. In particular, convolutional neural networks (CNN) generate a keen…
We introduce a novel convolutional neural network architecture, termed the \emph{periodic CNN}, which incorporates periodic boundary conditions into the convolutional layers. Our main theoretical contribution is a rigorous approximation…