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We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$,…

Machine Learning · Computer Science 2023-06-26 Matthew Wicker , Andrea Patane , Luca Laurenti , Marta Kwiatkowska

Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly…

Systems and Control · Electrical Eng. & Systems 2026-04-02 Neelay Junnarkar , Yasin Sonmez , Murat Arcak

Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…

Machine Learning · Computer Science 2023-09-06 Ruihan Zhang , Peixin Zhang , Jun Sun

This work addresses the certification of the local robustness of vision-based two-stage 6D object pose estimation. The two-stage method for object pose estimation achieves superior accuracy by first employing deep neural network-driven…

Computer Vision and Pattern Recognition · Computer Science 2024-08-02 Xusheng Luo , Tianhao Wei , Simin Liu , Ziwei Wang , Luis Mattei-Mendez , Taylor Loper , Joshua Neighbor , Casidhe Hutchison , Changliu Liu

Robustness verification of neural networks, referring to formally proving that neural networks satisfy robustness properties, is of crucial importance in safety-critical applications, where model failures can result in loss of human life or…

Machine Learning · Computer Science 2026-04-06 Minh Le , Phuong Cao

It is known that deep neural networks (DNNs) classify an input image by paying particular attention to certain specific pixels; a graphical representation of the magnitude of attention to each pixel is called a saliency-map. Saliency-maps…

Computer Vision and Pattern Recognition · Computer Science 2022-07-14 Satoshi Munakata , Caterina Urban , Haruki Yokoyama , Koji Yamamoto , Kazuki Munakata

Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…

Optimization and Control · Mathematics 2025-03-04 Yuhao Zhang , Xiangru Xu

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

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

Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…

Machine Learning · Computer Science 2021-03-30 Mehrnaz Najafi , Philip S. Yu

Verifying robustness of neural networks given a specified threat model is a fundamental yet challenging task. While current verification methods mainly focus on the $\ell_p$-norm threat model of the input instances, robustness verification…

Machine Learning · Computer Science 2020-06-16 Jeet Mohapatra , Tsui-Wei , Weng , Pin-Yu Chen , Sijia Liu , Luca Daniel

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

Graph neural networks (GNNs) achieve the state-of-the-art on graph-relevant tasks such as node and graph classification. However, recent works show GNNs are vulnerable to adversarial perturbations include the perturbation on edges, nodes,…

Cryptography and Security · Computer Science 2025-02-04 Jiate Li , Binghui Wang

Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…

Machine Learning · Computer Science 2022-09-01 Soumyabrata Talukder , Ratnesh Kumar

Training deep neural network classifiers that are certifiably robust against adversarial attacks is critical to ensuring the security and reliability of AI-controlled systems. Although numerous state-of-the-art certified training methods…

Machine Learning · Computer Science 2022-10-27 Pratik Vaishnavi , Kevin Eykholt , Amir Rahmati

The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…

Machine Learning · Computer Science 2022-01-13 Aounon Kumar , Tom Goldstein

In recent years, there has been significant attention given to the robustness assessment of neural networks. Robustness plays a critical role in ensuring reliable operation of artificial intelligence (AI) systems in complex and uncertain…

Computer Vision and Pattern Recognition · Computer Science 2024-04-16 Jie Wang , Jun Ai , Minyan Lu , Haoran Su , Dan Yu , Yutao Zhang , Junda Zhu , Jingyu Liu

Deep learning models are vulnerable to adversarial perturbations, raising important concerns for safety-critical deployment. Empirical defenses can achieve strong robustness in practice, but lack formal guarantees, motivating the need for…

Machine Learning · Computer Science 2026-05-26 Konstantinos Emmanouilidis , Tianjiao Ding , Nghia Nguyen , Nicolas Loizou , René Vidal

The success of neural networks across most machine learning tasks and the persistence of adversarial examples have made the verification of such models an important quest. Several techniques have been successfully developed to verify…

Machine Learning · Computer Science 2019-10-14 Nathanaël Fijalkow , Mohit Kumar Gupta

Deep neural networks (DNNs) are known to be vulnerable to adversarial geometric transformation. This paper aims to verify the robustness of large-scale DNNs against the combination of multiple geometric transformations with a provable…

Machine Learning · Computer Science 2023-04-03 Fu Wang , Peipei Xu , Wenjie Ruan , Xiaowei Huang