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Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU…

Machine Learning · Computer Science 2026-02-23 Yuhao Mao , Yani Zhang , Martin Vechev

Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race…

Machine Learning · Computer Science 2018-11-06 Aditi Raghunathan , Jacob Steinhardt , Percy Liang

While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are…

Machine Learning · Computer Science 2019-02-07 Sahil Singla , Soheil Feizi

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the…

Machine Learning · Computer Science 2020-10-26 Christian Tjandraatmadja , Ross Anderson , Joey Huchette , Will Ma , Krunal Patel , Juan Pablo Vielma

In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…

Machine Learning · Computer Science 2020-09-21 Brendon G. Anderson , Ziye Ma , Jingqi Li , Somayeh Sojoudi

Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but…

Machine Learning · Computer Science 2020-01-13 Hadi Salman , Greg Yang , Huan Zhang , Cho-Jui Hsieh , Pengchuan Zhang

The robustness of a neural network to adversarial examples can be provably certified by solving a convex relaxation. If the relaxation is loose, however, then the resulting certificate can be too conservative to be practically useful.…

Optimization and Control · Mathematics 2020-10-28 Richard Y. Zhang

There has been a rapid development and interest in adversarial training and defenses in the machine learning community in the recent years. One line of research focuses on improving the performance and efficiency of adversarial robustness…

Machine Learning · Computer Science 2022-12-07 Cheng Tang

In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…

Machine Learning · Computer Science 2025-05-13 Brendon G. Anderson , Ziye Ma , Jingqi Li , Somayeh Sojoudi

Adversarial robustness has become an emerging challenge for neural network owing to its over-sensitivity to small input perturbations. While being critical, we argue that solving this singular issue alone fails to provide a comprehensive…

Machine Learning · Computer Science 2021-03-02 Yu-Lin Tsai , Chia-Yi Hsu , Chia-Mu Yu , Pin-Yu Chen

The increasing integration of deep neural networks in critical systems has spawned a theoretical and practical interest in formally guaranteeing safety properties about their behavior. To achieve this, contemporary verification algorithms…

Logic in Computer Science · Computer Science 2026-05-29 Ido Shmuel , Guy Katz

Neural Networks (NNs) have increasingly apparent safety implications commensurate with their proliferation in real-world applications: both unanticipated as well as adversarial misclassifications can result in fatal outcomes. As a…

Machine Learning · Computer Science 2021-04-20 Haitham Khedr , James Ferlez , Yasser Shoukry

The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by…

Optimization and Control · Mathematics 2023-10-10 Brendon G. Anderson , Samuel Pfrommer , Somayeh Sojoudi

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

It is well-known that deep neural networks are vulnerable to adversarial attacks. Recent studies show that well-designed classification parts can lead to better robustness. However, there is still much space for improvement along this line.…

Machine Learning · Computer Science 2020-10-09 Cong Xu , Dan Li , Min Yang

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…

Machine Learning · Computer Science 2023-06-16 Hong-Ming Chiu , Richard Y. Zhang

Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to adversarial attacks, which have brought great concerns when…

Machine Learning · Computer Science 2023-04-13 Linyi Li , Tao Xie , Bo Li

The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing…

Machine Learning · Computer Science 2026-05-13 Sara Taheri , Mahalakshmi Sabanayagam , Debarghya Ghoshdastidar , Majid Zamani

The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While…

Machine Learning · Computer Science 2022-03-29 Zhilu Wang , Chao Huang , Qi Zhu

Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial…

Machine Learning · Computer Science 2021-02-02 Anian Ruoss , Maximilian Baader , Mislav Balunović , Martin Vechev
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