Safety Verification of Deep Neural Networks

Xiaowei Huang, Marta Kwiatkowska, Sen Wang, Min Wu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

532 Citations (Scopus)
173 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationComputer Aided Verification (CAV)
EditorsRupak Majumdar, Viktor Kunčak
Number of pages27
ISBN (Electronic)9783319633879
ISBN (Print)9783319633862
Publication statusPublished - 13 Jul 2017

Publication series

NameLecture Notes in Computer Science
NumberPart 1
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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