相关论文: Guaranteed Recovery of One-Hidden-Layer Neural Net…

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on…

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. However, the theoretical foundations underlying their…

We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to…

In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

Recently, deep learning models have achieved great success in computer vision applications, relying on large-scale class-balanced datasets. However, imbalanced class distributions still limit the wide applicability of these models due to…

In this article we study fully-connected feedforward deep ReLU ANNs with an arbitrarily large number of hidden layers and we prove convergence of the risk of the GD optimization method with random initializations in the training of such…

A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite…

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…

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…

In this work, we study the training and generalization performance of two-layer neural networks (NNs) after one gradient descent step under structured data modeled by Gaussian mixtures. While previous research has extensively analyzed this…

The Graph Convolutional Networks (GCN) proposed by Kipf and Welling is an effective model for semi-supervised learning, but faces the obstacle of over-smoothing, which will weaken the representation ability of GCN. Recently some works are…

Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for…

Generative neural networks have been empirically found very promising in providing effective structural priors for compressed sensing, since they can be trained to span low-dimensional data manifolds in high-dimensional signal spaces.…

Advanced machine learning methods, and more prominently neural networks, have become standard to solve inverse problems over the last years. However, the theoretical recovery guarantees of such methods are still scarce and difficult to…

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

Monocular depth estimation, which plays a key role in understanding 3D scene geometry, is fundamentally an ill-posed problem. Existing methods based on deep convolutional neural networks (DCNNs) have examined this problem by learning…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We examine the theoretical properties of enforcing priors provided by generative deep neural networks via empirical risk minimization. In particular we consider two models, one in which the task is to invert a generative neural network…

In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study…