相关论文: Learning Brenier Potentials with Convex Generative…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…
In this work, we analyze the capabilities and practical limitations of neural networks (NNs) for sequence-based signal processing which can be seen as an omnipresent property in almost any modern communication systems. In particular, we…
The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…
In this paper, we describe a phenomenon, which we named "super-convergence", where neural networks can be trained an order of magnitude faster than with standard training methods. The existence of super-convergence is relevant to…
Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of…
Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…
With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…
This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…
The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…
We consider the fundamental problem of ReLU regression, where the goal is to output the best fitting ReLU with respect to square loss given access to draws from some unknown distribution. We give the first efficient, constant-factor…
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the…
We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However,…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
Generative Adversarial Networks (GANs) are one of the most popular tools for learning complex high dimensional distributions. However, generalization properties of GANs have not been well understood. In this paper, we analyze the…
While deep neural networks have achieved remarkable success in various computer vision tasks, they often fail to generalize to new domains and subtle variations of input images. Several defenses have been proposed to improve the robustness…
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models…
The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…
In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the…
This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These neural networks are simple because they are designed with a…
Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn…