Related papers: Rethinking Neural-based Matrix Inversion: Why can'…

We construct a Neural Network that approximates the matrix multiplication operator for any activation function such that there exists a Neural Network which can approximate the scalar multiplication function. In particular, we use the…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

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…

Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives lower bounds on how well we can approximate the functions in K when requiring the approximants to…

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fr\'echet space $\X$ into a Banach space $\Y$. The…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a…

Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…

Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…

One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive growth of the number of parameters, which, in turn, leads…

Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…

Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…

Training a neural network using backpropagation algorithm requires passing error gradients sequentially through the network. The backward locking prevents us from updating network layers in parallel and fully leveraging the computing…

Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far…

The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid…