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Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation…

Machine Learning · Computer Science 2023-04-13 Zhuolin Yang , Zhikuan Zhao , Boxin Wang , Jiawei Zhang , Linyi Li , Hengzhi Pei , Bojan Karlas , Ji Liu , Heng Guo , Ce Zhang , Bo Li

Lipschitz bounded neural networks are certifiably robust and have a good trade-off between clean and certified accuracy. Existing Lipschitz bounding methods train from scratch and are limited to moderately sized networks (< 6M parameters).…

Computer Vision and Pattern Recognition · Computer Science 2023-02-22 Kavya Gupta , Sagar Verma

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded…

Machine Learning · Computer Science 2019-07-15 Chen Liu , Ryota Tomioka , Volkan Cevher

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

Data errors, corruptions, and poisoning attacks during training pose a major threat to the reliability of modern AI systems. While extensive effort has gone into empirical mitigations, the evolving nature of attacks and the complexity of…

Machine Learning · Computer Science 2025-10-28 Tobias Lorenz , Marta Kwiatkowska , Mario Fritz

This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability…

Machine Learning · Computer Science 2021-09-23 María Pérez-Ortiz , Omar Rivasplata , John Shawe-Taylor , Csaba Szepesvári

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…

Computer Vision and Pattern Recognition · Computer Science 2018-11-02 Yusuke Tsuzuku , Issei Sato , Masashi Sugiyama

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

Machine Learning · Computer Science 2019-12-20 Aleksandar Bojchevski , Stephan Günnemann

A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network…

Machine Learning · Computer Science 2021-12-13 Maria Perez-Ortiz , Omar Rivasplata , Emilio Parrado-Hernandez , Benjamin Guedj , John Shawe-Taylor

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…

Machine Learning · Computer Science 2024-05-01 Ge Yan , Yaniv Romano , Tsui-Wei Weng

Existing certified training methods can only train models to be robust against a certain perturbation type (e.g. $l_\infty$ or $l_2$). However, an $l_\infty$ certifiably robust model may not be certifiably robust against $l_2$ perturbation…

Machine Learning · Computer Science 2026-04-15 Enyi Jiang , David S. Cheung , Gagandeep Singh

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…

Machine Learning · Computer Science 2025-08-27 Rudy Bunel , Jingyue Lu , Ilker Turkaslan , Philip H. S. Torr , Pushmeet Kohli , M. Pawan Kumar

Robustness verification that aims to formally certify the prediction behavior of neural networks has become an important tool for understanding model behavior and obtaining safety guarantees. However, previous methods can usually only…

Machine Learning · Computer Science 2020-12-24 Zhouxing Shi , Huan Zhang , Kai-Wei Chang , Minlie Huang , Cho-Jui Hsieh

In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through…

Machine Learning · Computer Science 2022-10-13 Andrew C. Cullen , Paul Montague , Shijie Liu , Sarah M. Erfani , Benjamin I. P. Rubinstein

Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We…

Machine Learning · Computer Science 2021-02-03 Akhilan Boopathy , Tsui-Wei Weng , Sijia Liu , Pin-Yu Chen , Gaoyuan Zhang , Luca Daniel

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

We study the average robustness notion in deep neural networks in (selected) wide and narrow, deep and shallow, as well as lazy and non-lazy training settings. We prove that in the under-parameterized setting, width has a negative effect…

Machine Learning · Computer Science 2023-02-13 Zhenyu Zhu , Fanghui Liu , Grigorios G Chrysos , Volkan Cevher

Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks. A key challenge, supported both theoretically and empirically, is that robustness demands…

Machine Learning · Computer Science 2024-06-25 Kai Hu , Klas Leino , Zifan Wang , Matt Fredrikson

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

Continual learning under adversarial conditions remains an open problem, as existing methods often compromise either robustness, scalability, or both. We propose a novel framework that integrates Interval Bound Propagation (IBP) with a…

Machine Learning · Computer Science 2025-11-24 Patryk Krukowski , Łukasz Gorczyca , Piotr Helm , Kamil Książek , Przemysław Spurek