Related papers: Approximation bounds for convolutional neural netw…

We study the approximation rates of a class of deep neural network approximations of operators which arise as data-to-solution maps $\mathcal{S}$ of linear elliptic partial differential equations (PDEs), and act between pairs $X,Y$ of…

In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…

We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solution of partial differential equations (PDEs), and are used in…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…

In this paper, we explain the universal approximation capabilities of deep residual neural networks through geometric nonlinear control. Inspired by recent work establishing links between residual networks and control systems, we provide a…

Convolutional neural networks (CNNs) have been employed along with Variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. In order to do so, however, a CNN with only linearly many…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…

This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount of training data. Concretely, we consider Kolmogorov-optimal…

The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly…

We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms. First, we construct, based on a calculus of ReLU networks, artificial neural networks with ReLU activation…

The existence of adversarial examples is relatively understood for random fully connected neural networks, but much less so for convolutional neural networks (CNNs). The recent work [Daniely, 2025] establishes that adversarial examples can…

This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…

Neural Processes (NPs) are meta-learning models that learn to map sets of observations to approximations of the corresponding posterior predictive distributions. By accommodating variable-sized, unstructured collections of observations and…

In a previous work we have detailed the requirements to obtain a maximal performance benefit by implementing fully connected deep neural networks (DNN) in form of arrays of resistive devices for deep learning. This concept of Resistive…