相关论文: Lipschitz-aware Linearity Grafting for Certified R…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

Recent research has established that the local Lipschitz constant of a neural network directly influences its adversarial robustness. We exploit this relationship to construct an ensemble of neural networks which not only improves the…

Probabilistic learning is increasingly being tackled as an optimization problem, with gradient-based approaches as predominant methods. When modelling multivariate likelihoods, a usual but undesirable outcome is that the learned model fits…

Lipschitz constants of neural networks allow for guarantees of robustness in image classification, safety in controller design, and generalizability beyond the training data. As calculating Lipschitz constants is NP-hard, techniques for…

The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network. We introduce a semidefinite programming hierarchy to…

Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system,…

Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…

In binary classification and regression problems, it is well understood that Lipschitz continuity and smoothness of the loss function play key roles in governing generalization error bounds for empirical risk minimization algorithms. In…

Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this…

Recent years have seen growing interest in developing and applying perceptual similarity metrics. Research has shown the superiority of perceptual metrics over pixel-wise metrics in aligning with human perception and serving as a proxy for…

Neural networks are often highly sensitive to input and weight perturbations. This sensitivity has been linked to pathologies such as vulnerability to adversarial examples, divergent training, and overfitting. To combat these problems, past…

As the representations output by Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes important to ensure that these representations are fair and stable. In this work, we establish a key connection…

Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…

This paper introduces a promising alternative method for training Generative Adversarial Networks (GANs) on large-scale datasets with clear theoretical guarantees. GANs are typically learned through a minimax game between a generator and a…

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…

This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of…

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial…

Since the Lipschitz properties of convolutional neural networks (CNNs) are widely considered to be related to adversarial robustness, we theoretically characterize the $\ell_1$ norm and $\ell_\infty$ norm of 2D multi-channel convolutional…

Current approaches to novelty or anomaly detection are based on deep neural networks. Despite their effectiveness, neural networks are also vulnerable to imperceptible deformations of the input data. This is a serious issue in critical…

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…