# Safety Verification of Deep Neural Networks Source: [Safety Verification of Deep Neural Networks]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:33.579Z Authors: Xiaowei Huang, Marta Kwiatkowska, Sen Wang, Min Wu Published: 2016-10-21T20:16:16.000Z ## Abstract Deep neural networks have achieved impressive experimental results in image classification, but can surprisingly be unstable with respect to adversarial perturbations, that is, minimal changes to the input image that cause the network to misclassify it. With potential applications including perception modules and end-to-end controllers for self-driving cars, this raises concerns about their safety. We develop a novel automated verification framework for feed-forward multi-layer neural networks based on Satisfiability Modulo Theory (SMT). We focus on safety of image classification decisions with respect to image manipulations, such as scratches or changes to camera angle or lighting conditions that would result in the same class being assigned by a human, and define safety for an individual decision in terms of invariance of the classification within a small neighbourhood of the original image. We enable exhaustive search of the region by employing discretisation, and propagate the analysis layer by layer. Our method works directly with the network code and, in contrast to existing methods, can guarantee that adversarial examples, if they exist, are found for the given region and family of manipulations. If found, adversarial examples can be shown to human testers and/or used to fine-tune the network. We implement the techniques using Z3 and evaluate them on state-of-the-art networks, including regularised and deep learning networks. We also compare against existing techniques to search for adversarial examples and estimate network robustness. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Robustness Verification on Iris dataset (test)](): Robustness Verification; Iris dataset (test); Vulnerable Samples: 0. - [Robustness Verification on make\_moons](): Robustness Verification; make\_moons; Certified Accuracy (eps=0.05): 100. ## Original sources and implementation [Original paper]() [PDF]()