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Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system,…

Systems and Control · Electrical Eng. & Systems 2022-11-14 Matthew Cleaveland , Lars Lindemann , Radoslav Ivanov , George Pappas

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

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

Relying on the premise that the performance of a binary neural network can be largely restored with eliminated quantization error between full-precision weight vectors and their corresponding binary vectors, existing works of network…

Machine Learning · Computer Science 2022-07-19 Yuzhang Shang , Dan Xu , Bin Duan , Ziliang Zong , Liqiang Nie , Yan Yan

Reinforcement Learning (RL) has achieved remarkable success in safety-critical areas, but it can be weakened by adversarial attacks. Recent studies have introduced "smoothed policies" in order to enhance its robustness. Yet, it is still…

Machine Learning · Computer Science 2023-12-13 Ronghui Mu , Leandro Soriano Marcolino , Tianle Zhang , Yanghao Zhang , Xiaowei Huang , Wenjie Ruan

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

Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips…

Machine Learning · Computer Science 2023-06-27 Pierre Osselin , Henry Kenlay , Xiaowen Dong

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

The study of the expressive power of neural networks has investigated the fundamental limits of neural networks. Most existing results assume real-valued inputs and parameters as well as exact operations during the evaluation of neural…

Machine Learning · Computer Science 2024-07-17 Yeachan Park , Geonho Hwang , Wonyeol Lee , Sejun Park

While certified robustness is widely promoted as a solution to adversarial examples in Artificial Intelligence systems, significant challenges remain before these techniques can be meaningfully deployed in real-world applications. We…

Cryptography and Security · Computer Science 2025-08-12 Andrew C. Cullen , Paul Montague , Sarah M. Erfani , Benjamin I. P. Rubinstein

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

Machine Learning · Computer Science 2024-01-17 Fabien Geyer , Johannes Freitag , Tobias Schulz , Sascha Uhrig

As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…

Quantum Physics · Physics 2025-10-08 James Mills , Adithya Sireesh , Dominik Leichtle , Joschka Roffe , Elham Kashefi

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

Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…

Machine Learning · Computer Science 2019-02-19 Ravi Mangal , Aditya V. Nori , Alessandro Orso

With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…

Machine Learning · Computer Science 2019-01-08 Tsui-Wei Weng , Pin-Yu Chen , Lam M. Nguyen , Mark S. Squillante , Ivan Oseledets , Luca Daniel

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

This report presents a neurosymbolic framework for safety verification and control synthesis in high-dimensional monotone dynamical systems without relying on explicit models or conservative Lipschitz bounds. The approach combines the…

Systems and Control · Electrical Eng. & Systems 2026-01-28 Saber Jafarpour , Alireza Nadali , Ashutosh Trivedi , Majid Zamani

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…

Machine Learning · Computer Science 2024-05-16 Aref Miri Rekavandi , Olga Ohrimenko , Benjamin I. P. Rubinstein

Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high…

Machine Learning · Computer Science 2017-11-07 Matthias Hein , Maksym Andriushchenko

Barrier certificates play an important role in verifying the safety of continuous-time systems, including autonomous driving, robotic manipulators and other critical applications. Recently, ReLU neural barrier certificates -- barrier…

Systems and Control · Electrical Eng. & Systems 2025-11-14 Dejin Ren , Yiling Xue , Taoran Wu , Bai Xue