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We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean…

Machine Learning · Statistics 2026-04-20 Yulia Alexandr , Hao Duan , Guido Montúfar

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…

Machine Learning · Computer Science 2019-07-01 Daniel Zügner , Stephan Günnemann

Deep neural networks (DNNs) are vulnerable to adversarial attacks. It is found empirically that adversarially robust generalization is crucial in establishing defense algorithms against adversarial attacks. Therefore, it is interesting to…

Machine Learning · Computer Science 2023-10-31 Jiancong Xiao , Ruoyu Sun , Zhi- Quan Luo

Machine learning models are vulnerable to adversarial attacks. One approach to addressing this vulnerability is certification, which focuses on models that are guaranteed to be robust for a given perturbation size. A drawback of recent…

Machine Learning · Computer Science 2020-10-07 Ryan Campbell , Chris Finlay , Adam M Oberman

Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test…

Machine Learning · Computer Science 2019-10-18 Yogesh Balaji , Tom Goldstein , Judy Hoffman

The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on…

Machine Learning · Computer Science 2023-11-29 Bernd Prach , Fabio Brau , Giorgio Buttazzo , Christoph H. Lampert

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

Adversarial training is a powerful type of defense against adversarial examples. Previous empirical results suggest that adversarial training requires wider networks for better performances. However, it remains elusive how neural network…

Machine Learning · Computer Science 2021-08-17 Boxi Wu , Jinghui Chen , Deng Cai , Xiaofei He , Quanquan Gu

Adversarial examples bring a considerable security threat to support vector machines (SVMs), especially those used in safety-critical applications. Thus, robustness verification is an essential issue for SVMs, which can provide provable…

Machine Learning · Computer Science 2023-06-06 Yuting Liu , Hong Gu , Pan Qin

Neural networks are part of many contemporary NLP systems, yet their empirical successes come at the price of vulnerability to adversarial attacks. Previous work has used adversarial training and data augmentation to partially mitigate such…

Computation and Language · Computer Science 2019-12-23 Po-Sen Huang , Robert Stanforth , Johannes Welbl , Chris Dyer , Dani Yogatama , Sven Gowal , Krishnamurthy Dvijotham , Pushmeet Kohli

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

Machine Learning · Computer Science 2021-05-13 Anna-Kathrin Kopetzki , Stephan Günnemann

The rise of computer vision applications in the real world puts the security of the deep neural networks at risk. Recent works demonstrate that convolutional neural networks are susceptible to adversarial examples - where the input images…

Computer Vision and Pattern Recognition · Computer Science 2024-08-22 Sina Hajer Ahmadi , Hassan Bahrami

In the last a few decades, deep neural networks have achieved remarkable success in machine learning, computer vision, and pattern recognition. Recent studies however show that neural networks (both shallow and deep) may be easily fooled by…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 Zhuang Qian , Kaizhu Huang , Qiu-Feng Wang , Xu-Yao Zhang

The existence of adversarial examples poses a real danger when deep neural networks are deployed in the real world. The go-to strategy to quantify this vulnerability is to evaluate the model against specific attack algorithms. This approach…

Machine Learning · Computer Science 2021-06-08 Kevin Roth

The easiness at which adversarial instances can be generated in deep neural networks raises some fundamental questions on their functioning and concerns on their use in critical systems. In this paper, we draw a connection between…

Machine Learning · Computer Science 2018-03-02 Mahdieh Abbasi , Christian Gagné

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…

Machine Learning · Computer Science 2019-03-11 Francesco Croce , Maksym Andriushchenko , Matthias Hein

While deep learning has led to remarkable results on a number of challenging problems, researchers have discovered a vulnerability of neural networks in adversarial settings, where small but carefully chosen perturbations to the input can…

Neural and Evolutionary Computing · Computer Science 2018-11-26 Edward Grefenstette , Robert Stanforth , Brendan O'Donoghue , Jonathan Uesato , Grzegorz Swirszcz , Pushmeet Kohli

Adversarial vulnerability in vision and hallucination in large language models are conventionally viewed as separate problems, each addressed with modality-specific patches. This study first reveals that they share a common geometric…

Machine Learning · Computer Science 2026-03-30 Dong-Xiao Zhang , Hu Lou , Jun-Jie Zhang , Jun Zhu , Deyu Meng

Recent research studies revealed that neural networks are vulnerable to adversarial attacks. State-of-the-art defensive techniques add various adversarial examples in training to improve models' adversarial robustness. However, these…

Machine Learning · Computer Science 2019-09-13 Chang Song , Zuoguan Wang , Hai Li

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

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