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We study the problem of learning verifiably Lyapunov-stable neural controllers that provably satisfy the Lyapunov asymptotic stability condition within a region-of-attraction (ROA). Unlike previous works that adopted counterexample-guided…

Machine Learning · Computer Science 2026-04-07 Zhouxing Shi , Haoyu Li , Cho-Jui Hsieh , Huan Zhang

This paper proposes a novel, abstraction-based, certified training method for robust image classifiers. Via abstraction, all perturbed images are mapped into intervals before feeding into neural networks for training. By training on…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Zhaodi Zhang , Zhiyi Xue , Yang Chen , Si Liu , Yueling Zhang , Jing Liu , Min Zhang

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time…

Machine Learning · Computer Science 2023-08-22 Gaspard Lambrechts , Florent De Geeter , Nicolas Vecoven , Damien Ernst , Guillaume Drion

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded…

Machine Learning · Statistics 2020-02-19 Huijie Feng , Chunpeng Wu , Guoyang Chen , Weifeng Zhang , Yang Ning

As reinforcement learning (RL) has achieved near human-level performance in a variety of tasks, its robustness has raised great attention. While a vast body of research has explored test-time (evasion) attacks in RL and corresponding…

Machine Learning · Computer Science 2022-03-17 Fan Wu , Linyi Li , Chejian Xu , Huan Zhang , Bhavya Kailkhura , Krishnaram Kenthapadi , Ding Zhao , Bo Li

Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…

Machine Learning · Computer Science 2026-02-06 Wenting Li , Saif R. Kazi , Russell Bent , Duo Zhou , Huan Zhang

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower…

Machine Learning · Computer Science 2023-04-07 Dimitris Bertsimas , Xavier Boix , Kimberly Villalobos Carballo , Dick den Hertog

As spiking neural networks (SNNs) are deployed increasingly in real-world efficiency critical applications, the security concerns in SNNs attract more attention. Currently, researchers have already demonstrated an SNN can be attacked with…

Neural and Evolutionary Computing · Computer Science 2022-05-04 Ling Liang , Kaidi Xu , Xing Hu , Lei Deng , Yuan Xie

A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…

Machine Learning · Computer Science 2020-06-02 Sahil Singla , Soheil Feizi

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

Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness…

Machine Learning · Computer Science 2025-08-06 Lukas Koller , Tobias Ladner , Matthias Althoff

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

Training certifiably robust neural networks remains a notoriously hard problem. On one side, adversarial training optimizes under-approximations of the worst-case loss, which leads to insufficient regularization for certification, while on…

Machine Learning · Computer Science 2023-10-26 Yuhao Mao , Mark Niklas Müller , Marc Fischer , Martin Vechev

Making neural networks robust against adversarial inputs has resulted in an arms race between new defenses and attacks. The most promising defenses, adversarially robust training and verifiably robust training, have limitations that…

Machine Learning · Computer Science 2018-12-04 Shiqi Wang , Yizheng Chen , Ahmed Abdou , Suman Jana

Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…

Machine Learning · Computer Science 2023-01-26 Brendon G. Anderson , Somayeh Sojoudi

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

As reinforcement learning (RL) has achieved great success and been even adopted in safety-critical domains such as autonomous vehicles, a range of empirical studies have been conducted to improve its robustness against adversarial attacks.…

Machine Learning · Computer Science 2022-03-17 Fan Wu , Linyi Li , Zijian Huang , Yevgeniy Vorobeychik , Ding Zhao , Bo Li

Current SOTA adversarially robust models are mostly based on adversarial training (AT) and differ only by some regularizers either at inner maximization or outer minimization steps. Being repetitive in nature during the inner maximization…

Machine Learning · Computer Science 2021-11-02 Anindya Sarkar , Anirban Sarkar , Sowrya Gali , Vineeth N Balasubramanian

To obtain, deterministic guarantees of adversarial robustness, specialized training methods are used. We propose, SABR, a novel such certified training method, based on the key insight that propagating interval bounds for a small but…

Machine Learning · Computer Science 2023-03-10 Mark Niklas Müller , Franziska Eckert , Marc Fischer , Martin Vechev

Adversarial training is arguably the most popular way to provide empirical robustness against specific adversarial examples. While variants based on multi-step attacks incur significant computational overhead, single-step variants are…

Machine Learning · Computer Science 2025-03-25 Alessandro De Palma , Serge Durand , Zakaria Chihani , François Terrier , Caterina Urban