相关论文: The Geometry of Over-parameterized Regression and …

Graph contrastive learning is the state-of-the-art unsupervised graph representation learning framework and has shown comparable performance with supervised approaches. However, evaluating whether the graph contrastive learning is robust to…

In reality, learning from multi-view multi-label data inevitably confronts three challenges: missing labels, incomplete views, and non-aligned views. Existing methods mainly concern the first two and commonly need multiple assumptions to…

A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario,…

Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…

Generating adversarial examples is an intriguing problem and an important way of understanding the working mechanism of deep neural networks. Most existing approaches generated perturbations in the image space, i.e., each pixel can be…

Many machine learning image classifiers are vulnerable to adversarial attacks, inputs with perturbations designed to intentionally trigger misclassification. Current adversarial methods directly alter pixel colors and evaluate against pixel…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

Overparametrized models can exhibit an excellent generalization performance, although they should be prone to overfitting according to classical statistical theory. The discovery of the "double descent", indicating that the generalization…

Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization…

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schemes as well as general…

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

This work investigates adversarial training in the context of margin-based linear classifiers in the high-dimensional regime where the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha = n / d$. We introduce…

Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples. In this work we focus on two-layer neural networks trained using data which lie on a low…

Deep neural networks (DNNs) are notoriously vulnerable to adversarial attacks that place carefully crafted perturbations on normal examples to fool DNNs. To better understand such attacks, a characterization of the features carried by…

It has been shown that most machine learning algorithms are susceptible to adversarial perturbations. Slightly perturbing an image in a carefully chosen direction in the image space may cause a trained neural network model to misclassify…