Related papers: Universal Approximation Property of Fully Convolut…
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…
Deep convolutional neural networks (CNN) have recently been shown in many computer vision and pattern recog- nition applications to outperform by a significant margin state- of-the-art solutions that use traditional hand-crafted features.…
Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classification context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed,…
Deep convolutional neural networks (CNN) brought revolution without any doubt to various challenging tasks, mainly in computer vision. However, their model designing still requires attention to reduce number of learnable parameters, with no…
The latest generation of Convolutional Neural Networks (CNN) have achieved impressive results in challenging benchmarks on image recognition and object detection, significantly raising the interest of the community in these methods.…
In recent years, the research community has discovered that deep neural networks (DNNs) and convolutional neural networks (CNNs) can yield higher accuracy than all previous solutions to a broad array of machine learning problems. To our…
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…
We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has…
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…
We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory…
We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value…
We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…
We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends on two structural parameters which determine the numbers of…
While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can…
In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the…
Given the outstanding progress that convolutional neural networks (CNNs) have made on natural image classification and object recognition problems, it is shown that deep learning methods can achieve very good recognition performance on many…
Convolutional Neural Networks (CNNs) have begun to permeate all corners of electronic society (from voice recognition to scene generation) due to their high accuracy and machine efficiency per operation. At their core, CNN computations are…
Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. However, a very deep CNN…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…
An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…