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Sensitivity-based robustness certification has emerged as a practical approach for certifying neural network robustness, including in settings that require verifiable guarantees. A key advantage of these methods is that certification is…

Machine Learning · Computer Science 2026-03-26 Toby Murray

Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal…

Machine Learning · Computer Science 2026-05-14 Blaise Delattre , Hengyu Wu , Paul Caillon , Wei Yang Bryan Lim , Yang Cao

Adversarial examples pose a security threat to many critical systems built on neural networks. While certified training improves robustness, it also decreases accuracy noticeably. Despite various proposals for addressing this issue, the…

Machine Learning · Statistics 2024-06-21 Ruihan Zhang , Jun Sun

Randomized smoothing-based certification is an effective approach for obtaining robustness certificates of deep neural networks (DNNs) against adversarial attacks. This method constructs a smoothed DNN model and certifies its robustness…

Machine Learning · Computer Science 2024-04-12 Shubham Ugare , Tarun Suresh , Debangshu Banerjee , Gagandeep Singh , Sasa Misailovic

Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…

Machine Learning · Computer Science 2023-07-18 Aounon Kumar , Alexander Levine , Tom Goldstein , Soheil Feizi

Noise injection-based method has been shown to be able to improve the robustness of artificial neural networks in previous work. In this work, we propose a novel noise injection-based training scheme for better model robustness.…

Machine Learning · Computer Science 2023-05-30 Zeliang Zhang , Jinyang Jiang , Minjie Chen , Zhiyuan Wang , Yijie Peng , Zhaofei Yu

Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be…

Quantum Physics · Physics 2021-10-01 Ji Guan , Wang Fang , Mingsheng Ying

Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Paul Hamelbeck , Johannes Schiffer

We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…

Optimization and Control · Mathematics 2026-02-25 Alexander J Gallo , Massimiliano Zoggia , Alessandro Falsone , Maria Prandini , Simone Garatti

In recent years, neural networks have demonstrated outstanding effectiveness in a large amount of applications.However, recent works have shown that neural networks are susceptible to adversarial examples, indicating possible flaws…

Machine Learning · Computer Science 2018-06-08 Fuxun Yu , Zirui Xu , Yanzhi Wang , Chenchen Liu , Xiang Chen

Although large language models (LLMs) have achieved great success in vast real-world applications, their vulnerabilities towards noisy inputs have significantly limited their uses, especially in high-stake environments. In these contexts,…

Computation and Language · Computer Science 2023-07-17 Zhen Zhang , Guanhua Zhang , Bairu Hou , Wenqi Fan , Qing Li , Sijia Liu , Yang Zhang , Shiyu Chang

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

Machine Learning · Computer Science 2020-02-25 Chen Zhu , Renkun Ni , Ping-yeh Chiang , Hengduo Li , Furong Huang , Tom Goldstein

The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness, which captures the…

Machine Learning · Computer Science 2021-06-15 Klas Leino , Zifan Wang , Matt Fredrikson

Consistency regularization is a commonly-used technique for semi-supervised and self-supervised learning. It is an auxiliary objective function that encourages the prediction of the network to be similar in the vicinity of the observed…

Machine Learning · Computer Science 2021-10-05 Erik Englesson , Hossein Azizpour

Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…

Machine Learning · Computer Science 2019-08-20 Yuh-Shyang Wang , Tsui-Wei Weng , Luca Daniel

Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that…

Machine Learning · Computer Science 2019-02-19 Vincent Tjeng , Kai Xiao , Russ Tedrake

From an engineering perspective, a design should not only perform well in an ideal condition, but should also resist noises. Such a design methodology, namely robust design, has been widely implemented in the industry for product quality…

Machine Learning · Computer Science 2021-12-09 Jia-Qi Yang , Ke-Bin Fan , Hao Ma , De-Chuan Zhan

A range of defense methods have been proposed to improve the robustness of neural networks on adversarial examples, among which provable defense methods have been demonstrated to be effective to train neural networks that are certifiably…

Machine Learning · Computer Science 2021-01-21 Mengting Xu , Tao Zhang , Zhongnian Li , Daoqiang Zhang

Adversarial examples pose a security risk as they can alter decisions of a machine learning classifier through slight input perturbations. Certified robustness has been proposed as a mitigation where given an input $\mathbf{x}$, a…

Cryptography and Security · Computer Science 2024-09-10 Jiankai Jin , Olga Ohrimenko , Benjamin I. P. Rubinstein

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

Machine Learning · Computer Science 2026-03-03 Wenxin Li , Wenchao Liu , Chuan Wang , Qi Gao , Yin Ma , Hai Wei , Kai Wen