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We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…

The increasing use of deep neural networks for safety-critical applications, such as autonomous driving and flight control, raises concerns about their safety and reliability. Formal verification can address these concerns by guaranteeing…

With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…

Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…

The success of neural networks across most machine learning tasks and the persistence of adversarial examples have made the verification of such models an important quest. Several techniques have been successfully developed to verify…

Formal verification is a rigorous approach that can provably ensure the quality of neural networks, and to date, Branch and Bound (BaB) is the state-of-the-art that performs verification by splitting the problem as needed and applying…

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…

Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a…

Neural networks achieved high performance over different tasks, i.e. image identification, voice recognition and other applications. Despite their success, these models are still vulnerable regarding small perturbations, which can be used…

In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…

We study the problem of formal verification of Binarized Neural Networks (BNN), which have recently been proposed as a energy-efficient alternative to traditional learning networks. The verification of BNNs, using the reduction to hardware…

Formal verification provides critical security assurances for neural networks, yet its practical application suffers from the long verification time. This work introduces a novel method for training verification-friendly neural networks,…

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…

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…

Neural networks are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of…

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.…

Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…

Recently, formal verification of deep neural networks (DNNs) has garnered considerable attention, and over-approximation based methods have become popular due to their effectiveness and efficiency. However, these strategies face challenges…