相关论文: Gradient Methods Provably Converge to Non-Robust N…

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race…

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training neural networks with certifiable robustness guarantees when potential adversarial perturbations present, while the convergence of IBP training…

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…

In this paper we aim to explore the general robustness of neural network classifiers by utilizing adversarial as well as natural perturbations. Different from previous works which mainly focus on studying the robustness of neural networks…

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed…

Robustness and generalization ability of machine learning models are of utmost importance in various application domains. There is a wide interest in efficient ways to analyze those properties. One important direction is to analyze…

Adversarial robustness corresponds to the susceptibility of deep neural networks to imperceptible perturbations made at test time. In the context of image tasks, many algorithms have been proposed to make neural networks robust to…

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of…

The adversarial robustness of a neural network mainly relies on two factors: model capacity and anti-perturbation ability. In this paper, we study the anti-perturbation ability of the network from the feature maps of convolutional layers.…

Neural Networks have been shown to be sensitive to common perturbations such as blur, Gaussian noise, rotations, etc. They are also vulnerable to some artificial malicious corruptions called adversarial examples. The adversarial examples…

In adversarial attacks to machine-learning classifiers, small perturbations are added to input that is correctly classified. The perturbations yield adversarial examples, which are virtually indistinguishable from the unperturbed input, and…

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common…

In this paper, we consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. First, we mathematically show that for such networks L2-regularized regression…

Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…

For a standard convolutional neural network, optimizing over the input pixels to maximize the score of some target class will generally produce a grainy-looking version of the original image. However, Santurkar et al. (2019) demonstrated…

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the…