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Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…

Machine Learning · Computer Science 2021-11-03 Yujia Huang , Huan Zhang , Yuanyuan Shi , J Zico Kolter , Anima Anandkumar

We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…

Machine Learning · Computer Science 2019-10-14 Matthew Willetts , Alexander Camuto , Stephen Roberts , Chris Holmes

In the last decade, motivated by the success of Deep Learning, the scientific community proposed several approaches to make the learning procedure of Neural Networks more effective. When focussing on the way in which the training data are…

Machine Learning · Computer Science 2021-06-22 Simone Marullo , Matteo Tiezzi , Marco Gori , Stefano Melacci

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

Testing remains the primary method to evaluate the accuracy of neural network perception systems. Prior work on the formal verification of neural network perception models has been limited to notions of local adversarial robustness for…

Machine Learning · Computer Science 2020-12-18 Chris R. Serrano , Pape M. Sylla , Michael A. Warren

Deep neural networks have become widely used, obtaining remarkable results in domains such as computer vision, speech recognition, natural language processing, audio recognition, social network filtering, machine translation, and…

Neural and Evolutionary Computing · Computer Science 2020-02-03 Divya Gopinath , Guy Katz , Corina S. Pasareanu , Clark Barrett

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern…

Logic in Computer Science · Computer Science 2017-08-03 Ruediger Ehlers

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Machine Learning · Computer Science 2025-09-30 Frederik Baymler Mathiesen , Nikolaus Vertovec , Francesco Fabiano , Luca Laurenti , Alessandro Abate

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts. To do so, we bridge the gap between hand-crafted specifications and realistic deployment settings by proposing a novel…

Modern deep neural network (DNN) trainings utilize various training techniques, e.g., nonlinear activation functions, batch normalization, skip-connections, etc. Despite their effectiveness, it is still mysterious how they help accelerate…

Machine Learning · Computer Science 2024-03-05 Cheng Chen , Junjie Yang , Yi Zhou

Training neural networks with verifiable robustness guarantees is challenging. Several existing approaches utilize linear relaxation based neural network output bounds under perturbation, but they can slow down training by a factor of…

Machine Learning · Computer Science 2019-11-28 Huan Zhang , Hongge Chen , Chaowei Xiao , Sven Gowal , Robert Stanforth , Bo Li , Duane Boning , Cho-Jui Hsieh

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

Validation accuracy is a necessary, but not sufficient, measure of a neural network classifier's quality. High validation accuracy during development does not guarantee that a model is free of serious flaws, such as vulnerability to…

Machine Learning · Computer Science 2019-10-08 John S. Hyatt , Michael S. Lee

While neural networks have achieved high accuracy on standard image classification benchmarks, their accuracy drops to nearly zero in the presence of small adversarial perturbations to test inputs. Defenses based on regularization and…

Machine Learning · Computer Science 2020-11-03 Aditi Raghunathan , Jacob Steinhardt , Percy Liang

Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…

Machine Learning · Computer Science 2024-03-13 Shaoru Chen , Lekan Molu , Mahyar Fazlyab

Complete verification of deep neural networks (DNNs) can exactly determine whether the DNN satisfies a desired trustworthy property (e.g., robustness, fairness) on an infinite set of inputs or not. Despite the tremendous progress to improve…

Machine Learning · Computer Science 2023-06-13 Shubham Ugare , Debangshu Banerjee , Sasa Misailovic , Gagandeep Singh

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

Neural networks are successfully used in a variety of applications, many of them having safety and security concerns. As a result researchers have proposed formal verification techniques for verifying neural network properties. While…

Cryptography and Security · Computer Science 2022-05-10 Youcheng Sun , Muhammad Usman , Divya Gopinath , Corina S. Păsăreanu

With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…

Computation and Language · Computer Science 2022-07-14 Marco Casadio , Ekaterina Komendantskaya , Verena Rieser , Matthew L. Daggitt , Daniel Kienitz , Luca Arnaboldi , Wen Kokke

Control Barrier Functions (CBFs) that provide formal safety guarantees have been widely used for safety-critical systems. However, it is non-trivial to design a CBF. Utilizing neural networks as CBFs has shown great success, but it…

Systems and Control · Electrical Eng. & Systems 2023-11-20 Xinyu Wang , Luzia Knoedler , Frederik Baymler Mathiesen , Javier Alonso-Mora
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