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We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…

Programming Languages · Computer Science 2021-04-22 Caterina Urban , Antoine Miné

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

Machine Learning · Computer Science 2024-06-11 Anahita Baninajjar , Ahmed Rezine , Amir Aminifar

There is great interest in using formal methods to guarantee the reliability of deep neural networks. However, these techniques may also be used to implant carefully selected input-output pairs. We present initial results on a novel…

Machine Learning · Computer Science 2020-08-05 Ivan Papusha , Rosa Wu , Joshua Brulé , Yanni Kouskoulas , Daniel Genin , Aurora Schmidt

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

Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are…

Machine Learning · Computer Science 2023-02-06 Tianhao Wei , Changliu Liu

Formal verification of neural networks is essential for their deployment in safety-critical areas. Many available formal verification methods have been shown to be instances of a unified Branch and Bound (BaB) formulation. We propose a…

Machine Learning · Computer Science 2019-12-04 Jingyue Lu , M. Pawan Kumar

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

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security,…

Machine Learning · Computer Science 2021-10-06 Aws Albarghouthi

Deep neural networks (DNNs) are widely used in real-world applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing…

Computer Vision and Pattern Recognition · Computer Science 2024-11-19 Yizhak Y. Elboher , Avraham Raviv , Yael Leibovich Weiss , Omer Cohen , Roy Assa , Guy Katz , Hillel Kugler

Training and running deep neural networks (NNs) often demands a lot of computation and energy-intensive specialized hardware (e.g. GPU, TPU...). One way to reduce the computation and power cost is to use binary weight NNs, but these are…

Machine Learning · Computer Science 2024-01-09 Theodore Aouad , Hugues Talbot

Optimal symbol detection for multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Conventional heuristic algorithms are either too complex to be practical or suffer from poor performance. Recently, several…

Information Theory · Computer Science 2020-02-11 Mathieu Goutay , Fayçal Ait Aoudia , Jakob Hoydis

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

Artificial Intelligence · Computer Science 2017-05-22 Guy Katz , Clark Barrett , David Dill , Kyle Julian , Mykel Kochenderfer

Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks…

Machine Learning · Computer Science 2021-03-15 Yedi Zhang , Zhe Zhao , Guangke Chen , Fu Song , Taolue Chen

In this paper, we consider the computational complexity of formally verifying the behavior of Rectified Linear Unit (ReLU) Neural Networks (NNs), where verification entails determining whether the NN satisfies convex polytopic…

Machine Learning · Computer Science 2021-03-26 James Ferlez , Yasser Shoukry

Neural network verification is a new and rapidly developing field of research. So far, the main priority has been establishing efficient verification algorithms and tools, while proper support from the programming language perspective has…

Deep neural networks are highly effective at a range of computational tasks. However, they tend to be computationally expensive, especially in vision-related problems, and also have large memory requirements. One of the most effective…

Computer Vision and Pattern Recognition · Computer Science 2018-04-10 Ameya Prabhu , Vishal Batchu , Sri Aurobindo Munagala , Rohit Gajawada , Anoop Namboodiri

Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…

Machine Learning · Computer Science 2022-12-16 Xingchao Liu , Xing Han , Na Zhang , Qiang Liu

Binary neural networks (BNNs) are increasingly deployed in edge computing applications due to their low hardware complexity and high energy efficiency. However, verifying the robustness of BNNs against input perturbations, including…

Emerging Technologies · Computer Science 2026-02-17 Rahul Singh , Seyran Saeedi , Zheng Zhang

Deep Neural Networks (DNNs) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs can have bugs and can be attacked. To address this, research has explored a wide-range of…

Machine Learning · Computer Science 2024-01-23 Hai Duong , ThanhVu Nguyen , Matthew Dwyer

A wide range of verification methods have been proposed to verify the safety properties of deep neural networks ensuring that the networks function correctly in critical applications. However, many well-known verification tools still…

Software Engineering · Computer Science 2023-08-15 Yuyi Zhong , Ruiwei Wang , Siau-Cheng Khoo