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An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…

Optimization and Control · Mathematics 2022-05-05 S. Gratton , S. Jerad , Ph. L. Toint

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…

Computer Vision and Pattern Recognition · Computer Science 2020-10-06 Sadaf Gulshad , Jan Hendrik Metzen , Arnold Smeulders

Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that…

Adversarial training has been widely studied in recent years due to its role in improving model robustness against adversarial attacks. This paper focuses on comparing different distributed adversarial training algorithms--including…

Machine Learning · Computer Science 2025-09-16 Ying Cao , Kun Yuan , Ali H. Sayed

Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper…

Machine Learning · Computer Science 2023-05-25 Haotian Gu , Xin Guo , Xinyu Li

Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in…

Optimization and Control · Mathematics 2025-10-14 Abdurakhmon Sadiev , Peter Richtárik , Ilyas Fatkhullin

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…

Computer Vision and Pattern Recognition · Computer Science 2020-12-03 Pranjal Awasthi , George Yu , Chun-Sung Ferng , Andrew Tomkins , Da-Cheng Juan

Neural networks are known to be highly sensitive to adversarial examples. These may arise due to different factors, such as random initialization, or spurious correlations in the learning problem. To better understand these factors, we…

Machine Learning · Statistics 2022-07-05 Elvis Dohmatob , Alberto Bietti

In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…

Optimization and Control · Mathematics 2023-12-12 Tejas Natu , Camille Castera , Jalal Fadili , Peter Ochs

Adversarial training is an effective method to improve the machine learning (ML) model robustness. Most existing studies typically consider the Rectified linear unit (ReLU) activation function and centralized training environments. In this…

Machine Learning · Computer Science 2025-12-05 Long Dang , Thushari Hapuarachchi , Kaiqi Xiong , Jing Lin

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small…

Optimization and Control · Mathematics 2025-10-24 Guangyi He , Tobias Sutter , Lukas Gonon

Randomized smoothing is a popular way of providing robustness guarantees against adversarial attacks: randomly-smoothed functions have a universal Lipschitz-like bound, allowing for robustness certificates to be easily computed. In this…

Machine Learning · Computer Science 2020-12-16 Alexander Levine , Aounon Kumar , Thomas Goldstein , Soheil Feizi

There has been considerable and growing interest in applying machine learning for cyber defenses. One promising approach has been to apply natural language processing techniques to analyze logs data for suspicious behavior. A natural…

Machine Learning · Computer Science 2020-07-30 Kai Steverson , Jonathan Mullin , Metin Ahiskali

Neural networks, being susceptible to adversarial attacks, should face a strict level of scrutiny before being deployed in critical or adversarial applications. This paper uses ideas from Chaos Theory to explain, analyze, and quantify the…

Machine Learning · Computer Science 2023-07-07 Jonathan S. Kent

Deep neural networks are susceptible to adversarial attacks due to the accumulation of perturbations in the feature level, and numerous works have boosted model robustness by deactivating the non-robust feature activations that cause model…

Computer Vision and Pattern Recognition · Computer Science 2023-03-27 Woo Jae Kim , Yoonki Cho , Junsik Jung , Sung-Eui Yoon

Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as…

Machine Learning · Statistics 2022-04-05 Adel Javanmard , Mahdi Soltanolkotabi

Adversarial training tends to result in models that are less accurate on natural (unperturbed) examples compared to standard models. This can be attributed to either an algorithmic shortcoming or a fundamental property of the training data…

Machine Learning · Computer Science 2021-07-02 Alireza Mousavi Hosseini , Amir Mohammad Abouei , Mohammad Hossein Rohban

Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike artificial models,…

Neural and Evolutionary Computing · Computer Science 2025-02-04 Konstantin Holzhausen , Mia Merlid , Håkon Olav Torvik , Anders Malthe-Sørenssen , Mikkel Elle Lepperød

As deep learning models are increasingly deployed in high-risk applications, robust defenses against adversarial attacks and reliable performance guarantees become paramount. Moreover, accuracy alone does not provide sufficient assurance or…

Machine Learning · Computer Science 2025-06-10 Jie Bao , Chuangyin Dang , Rui Luo , Hanwei Zhang , Zhixin Zhou

Adversarial examples have been shown to be the severe threat to deep neural networks (DNNs). One of the most effective adversarial defense methods is adversarial training (AT) through minimizing the adversarial risk $R_{adv}$, which…

Machine Learning · Computer Science 2020-06-17 Yiming Li , Baoyuan Wu , Yan Feng , Yanbo Fan , Yong Jiang , Zhifeng Li , Shutao Xia