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Concerned with the reliability of neural networks, researchers have developed verification techniques to prove their robustness. Most verifiers work with real-valued networks. Unfortunately, the exact (complete and sound) verifiers face…

Artificial Intelligence · Computer Science 2020-10-28 Kai Jia , Martin Rinard

With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known…

Machine Learning · Computer Science 2020-05-18 Mahum Naseer , Mishal Fatima Minhas , Faiq Khalid , Muhammad Abdullah Hanif , Osman Hasan , Muhammad Shafique

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

Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing…

Systems and Control · Computer Science 2019-06-05 Kyle D. Julian , Mykel J. Kochenderfer

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

Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…

Optimization and Control · Mathematics 2024-04-02 Haoruo Zhao , Hassan Hijazi , Haydn Jones , Juston Moore , Mathieu Tanneau , Pascal Van Hentenryck

In recent years, it has been found that neural networks can be easily fooled by adversarial examples, which is a potential safety hazard in some safety-critical applications. Many researchers have proposed various method to make neural…

Machine Learning · Computer Science 2018-04-24 Shuangtao Li , Yuanke Chen , Yanlin Peng , Lin Bai

We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks…

Machine Learning · Computer Science 2022-02-01 Chandresh Pravin , Ivan Martino , Giuseppe Nicosia , Varun Ojha

Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be…

Machine Learning · Computer Science 2023-11-14 Stefano Calzavara , Lorenzo Cazzaro , Giulio Ermanno Pibiri , Nicola Prezza

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

These lecture notes provide an introduction to the verification of neural networks from a theoretical perspective. We discuss feed-forward neural networks, recurrent neural networks, attention mechanisms, and transformers, together with…

Logic in Computer Science · Computer Science 2026-04-29 Benedikt Bollig

Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…

Machine Learning · Statistics 2021-05-11 Théo Lacombe , Yuichi Ike , Mathieu Carriere , Frédéric Chazal , Marc Glisse , Yuhei Umeda

Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…

Machine Learning · Computer Science 2023-01-06 Chelsea Sidrane , Sydney Katz , Anthony Corso , Mykel J. Kochenderfer

Recent works have tried to increase the verifiability of adversarially trained networks by running the attacks over domains larger than the original perturbations and adding various regularization terms to the objective. However, these…

Machine Learning · Computer Science 2023-06-01 Alessandro De Palma , Rudy Bunel , Krishnamurthy Dvijotham , M. Pawan Kumar , Robert Stanforth

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…

Computational Complexity · Computer Science 2026-05-29 Eric Alsmann , Martin Lange , Marco Sälzer

When data is generated by multiple sources, conventional training methods update models assuming equal reliability for each source and do not consider their individual data quality. However, in many applications, sources have varied levels…

Machine Learning · Computer Science 2025-02-17 Alexander Capstick , Francesca Palermo , Tianyu Cui , Payam Barnaghi

Artificial Neural Networks (ANNs) have demonstrated remarkable utility in various challenging machine learning applications. While formally verified properties of their behaviors are highly desired, they have proven notoriously difficult to…

Machine Learning · Computer Science 2020-10-05 Xuankang Lin , He Zhu , Roopsha Samanta , Suresh Jagannathan

Groundbreaking successes have been achieved by Deep Reinforcement Learning (DRL) in solving practical decision-making problems. Robotics, in particular, can involve high-cost hardware and human interactions. Hence, scrupulous evaluations of…

Artificial Intelligence · Computer Science 2020-10-20 Davide Corsi , Enrico Marchesini , Alessandro Farinelli

Noise injection-based method has been shown to be able to improve the robustness of artificial neural networks in previous work. In this work, we propose a novel noise injection-based training scheme for better model robustness.…

Machine Learning · Computer Science 2023-05-30 Zeliang Zhang , Jinyang Jiang , Minjie Chen , Zhiyuan Wang , Yijie Peng , Zhaofei Yu

Even though neural networks are being increasingly deployed in safety-critical control applications, it remains difficult to enforce constraints on their output, meaning that it is hard to guarantee safety in such settings. While many…

Machine Learning · Computer Science 2025-08-27 Long Kiu Chung , Shreyas Kousik