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We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of $L^p$ norms of NNs and their derivatives. When combined with…

Numerical Analysis · Mathematics 2025-10-01 Emil Haugen , Alexei Stepanenko , Anders C. Hansen

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

Deep Neural Networks (DNNs) have become key components of many safety-critical applications such as autonomous driving and medical diagnosis. However, DNNs have been shown suffering from poor robustness because of their susceptibility to…

Machine Learning · Computer Science 2020-07-28 Wenjie Wan , Zhaodi Zhang , Yiwei Zhu , Min Zhang , Fu Song

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…

Machine Learning · Computer Science 2025-08-27 Rudy Bunel , Jingyue Lu , Ilker Turkaslan , Philip H. S. Torr , Pushmeet Kohli , M. Pawan Kumar

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Machine Learning · Computer Science 2021-06-22 Nathan Dahlin , Krishna Chaitanya Kalagarla , Nikhil Naik , Rahul Jain , Pierluigi Nuzzo

Recent approaches in domain-specific named entity recognition (NER), such as biomedical NER, have shown remarkable advances. However, they still lack of faithfulness, producing erroneous predictions. We assume that knowledge of entities can…

Computation and Language · Computer Science 2024-06-11 Seoyeon Kim , Kwangwook Seo , Hyungjoo Chae , Jinyoung Yeo , Dongha Lee

Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…

Machine Learning · Computer Science 2021-10-04 Kai Jia , Martin Rinard

Deep neural networks (DNNs) are increasingly being employed in safety-critical systems, and there is an urgent need to guarantee their correctness. Consequently, the verification community has devised multiple techniques and tools for…

Logic in Computer Science · Computer Science 2022-08-30 Omri Isac , Clark Barrett , Min Zhang , Guy Katz

Inspired by recent successes with parallel optimization techniques for solving Boolean satisfiability, we investigate a set of strategies and heuristics that aim to leverage parallel computing to improve the scalability of neural network…

Logic in Computer Science · Computer Science 2020-08-24 Haoze Wu , Alex Ozdemir , Aleksandar Zeljić , Ahmed Irfan , Kyle Julian , Divya Gopinath , Sadjad Fouladi , Guy Katz , Corina Pasareanu , Clark Barrett

Deep Neural Networks (DNN) are crucial in approximating nonlinear functions across diverse applications, ranging from image classification to control. Verifying specific input-output properties can be a highly challenging task due to the…

Machine Learning · Computer Science 2025-07-22 Tianhao Wei , Hanjiang Hu , Luca Marzari , Kai S. Yun , Peizhi Niu , Xusheng Luo , Changliu Liu

Deep Neural Networks (DNNs) are powerful tools that have shown extraordinary results in many scenarios, ranging from pattern recognition to complex robotic problems. However, their intricate designs and lack of transparency raise safety…

Artificial Intelligence · Computer Science 2023-12-12 Luca Marzari , Gabriele Roncolato , Alessandro Farinelli

Despite the functional success of deep neural networks (DNNs), their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques…

Machine Learning · Computer Science 2021-03-24 Teodora Baluta , Zheng Leong Chua , Kuldeep S. Meel , Prateek Saxena

Deep neural networks (DNNs) are prominent due to their superior performance in many fields. The deep-learning-as-a-service (DLaaS) paradigm enables individuals and organizations (clients) to outsource their DNN learning tasks to the…

Cryptography and Security · Computer Science 2021-07-02 Boxiang Dong , Bo Zhang , Hui , Wang

Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks. However, many relevant properties, such as fairness or global robustness, pertain to the entire input space. If one applies…

Machine Learning · Computer Science 2025-11-20 Faried Abu Zaid , Daniel Neider , Mustafa Yalçıner

One major drawback of deep convolutional neural networks (CNNs) for use in safety critical applications is their black-box nature. This makes it hard to verify or monitor complex, symbolic requirements on already trained computer vision…

Computer Vision and Pattern Recognition · Computer Science 2022-03-15 Gesina Schwalbe , Christian Wirth , Ute Schmid

Deep neural networks (DNNs) play a crucial role in the field of machine learning, demonstrating state-of-the-art performance across various application domains. However, despite their success, DNN-based models may occasionally exhibit…

Machine Learning · Computer Science 2024-07-02 Guy Amir , Osher Maayan , Tom Zelazny , Guy Katz , Michael Schapira

Modern convolutional neural networks (CNNs) are known to be overconfident in terms of their calibration on unseen input data. That is to say, they are more confident than they are accurate. This is undesirable if the probabilities predicted…

Machine Learning · Computer Science 2021-12-03 Guoxuan Xia , Sangwon Ha , Tiago Azevedo , Partha Maji

Deep neural networks (DNNs) have been shown lack of robustness for the vulnerability of their classification to small perturbations on the inputs. This has led to safety concerns of applying DNNs to safety-critical domains. Several…

Machine Learning · Computer Science 2021-02-24 Jianlin Li , Pengfei Yang , Jiangchao Liu , Liqian Chen , Xiaowei Huang , Lijun Zhang

Deep neural networks (DNN) are prone to miscalibrated predictions, often exhibiting a mismatch between the predicted output and the associated confidence scores. Contemporary model calibration techniques mitigate the problem of…

Machine Learning · Computer Science 2022-12-21 Ramya Hebbalaguppe , Rishabh Patra , Tirtharaj Dash , Gautam Shroff , Lovekesh Vig

Deploying deep neural networks (DNNs) as core functions in autonomous driving creates unique verification and validation challenges. In particular, the continuous engineering paradigm of gradually perfecting a DNN-based perception can make…

Machine Learning · Computer Science 2021-09-28 Chih-Hong Cheng , Rongjie Yan