Related papers: An Optimal Transport Approach for Computing Advers…
While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the…
Modern machine learning algorithms perform poorly on adversarially manipulated data. Adversarial risk quantifies the error of classifiers in adversarial settings; adversarial classifiers minimize adversarial risk. In this paper, we analyze…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
Recent studies have demonstrated the vulnerability of deep convolutional neural networks against adversarial examples. Inspired by the observation that the intrinsic dimension of image data is much smaller than its pixel space dimension and…
Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples,…
Deep learning classifiers are now known to have flaws in the representations of their class. Adversarial attacks can find a human-imperceptible perturbation for a given image that will mislead a trained model. The most effective methods to…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
Deep Neural Networks (DNN) have been shown to be vulnerable to adversarial examples. Adversarial training (AT) is a popular and effective strategy to defend against adversarial attacks. Recent works (Benz et al., 2020; Xu et al., 2021; Tian…
Decision trees are a popular choice of explainable model, but just like neural networks, they suffer from adversarial examples. Existing algorithms for fitting decision trees robust against adversarial examples are greedy heuristics and…
The vulnerability of Deep Neural Networks to Adversarial Attacks has fuelled research towards building robust models. While most Adversarial Training algorithms aim at defending attacks constrained within low magnitude Lp norm bounds,…
Adversarial training has become one of the most effective methods for improving robustness of neural networks. However, it often suffers from poor generalization on both clean and perturbed data. In this paper, we propose a new algorithm,…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
We introduce a new class of optimal-transport-regularized divergences, $D^c$, constructed via an infimal convolution between an information divergence, $D$, and an optimal-transport (OT) cost, $C$, and study their use in distributionally…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
Despite the fact that adversarial training has become the de facto method for improving the robustness of deep neural networks, it is well-known that vanilla adversarial training suffers from daunting robust overfitting, resulting in…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
Adversarial training can improve the robustness of neural networks. Previous methods focus on a single adversarial training strategy and do not consider the model property trained by different strategies. By revisiting the previous methods,…
The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…