Artificial Neural networks (ANNs) are powerful computing systems employed for various applications due to their versatility to generalize and to respond to unexpected inputs patterns. However, implementations of ANNs for safety-critical systems might lead to failures, which are hardly predicted in the design phase since ANNs are highly parallel and their parameters are hardly interpretable. Here we develop and evaluate a novel symbolic software verification framework based on incremental bounded model checking (BMC) to check for adversarial cases and coverage methods in multi-layer perceptron (MLP). In particular, we further develop the efficient SMT-based Context-Bounded Model Checker for Graphical Processing Units (ESBMC-GPU) in order to ensure the reliability of certain safety properties in which safety-critical systems can fail and make incorrect decisions, thereby leading to unwanted material damage or even put lives in danger. This paper marks the first symbolic verification framework to reason over ANNs implemented in CUDA. Our experimental results show that our approach implemented in ESBMC-GPU can successfully verify safety properties and covering methods in ANNs and correctly generate 28 adversarial cases in MLPs.
@cite_34 and @cite_32 have shown how weak ANNs can be if small noises are present in their inputs. They described and evaluated testing and verification approaches based on covering methods and images proximity @cite_34 and how adversarial cases are obtained @cite_32 . In particular, our study resembles that of and @cite_32 @cite_34 to obtain adversarial cases. Here, if any property is violated, then a counterexample is provided; in cases of safety properties, adversarial examples will be generated via counterexample using ESBMC-GPU. In contrast to @cite_32 , we do not focus on generating noise in specific regions, but in every image pixel. Our approach in images proximity is influenced by @cite_34 but we use incremental BMC instead of concolic testing as our verification engine. Our symbolic verification method checks safety properties on non-deterministic images with a certain distance of a given image; both image and distance are determined by the user. @cite_2 also describe an approach to validate ANNs using symbolic execution by translating a NN into an imperative program. By contrast, we consider the actual implementation of ANN in CUDA and apply incremental BMC using off-the-shelf SMT solvers.
@cite_34 @cite_32 @cite_2
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Deep neural networks (DNNs) have a wide range of applications, and software employing them must be thoroughly tested, especially in safety-critical domains. However, traditional software test coverage metrics cannot be applied directly to DNNs. In this paper, inspired by the MC DC coverage criterion, we propose a family of four novel test criteria that are tailored to structural features of DNNs and their semantics. We validate the criteria by demonstrating that the generated test inputs guided via our proposed coverage criteria are able to capture undesired behaviours in a DNN. Test cases are generated using a symbolic approach and a gradient-based heuristic search. By comparing them with existing methods, we show that our criteria achieve a balance between their ability to find bugs (proxied using adversarial examples) and the computational cost of test case generation. Our experiments are conducted on state-of-the-art DNNs obtained using popular open source datasets, including MNIST, CIFAR-10 and ImageNet. 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. Deep Neural Networks (DNN) are increasingly used in a variety of applications, many of them with substantial safety and security concerns. This paper introduces DeepCheck, a new approach for validating DNNs based on core ideas from program analysis, specifically from symbolic execution. The idea is to translate a DNN into an imperative program, thereby enabling program analysis to assist with DNN validation. A basic translation however creates programs that are very complex to analyze. DeepCheck introduces novel techniques for lightweight symbolic analysis of DNNs and applies them in the context of image classification to address two challenging problems in DNN analysis: 1) identification of important pixels (for attribution and adversarial generation); and 2) creation of 1-pixel and 2-pixel attacks. Experimental results using the MNIST data-set show that DeepCheck's lightweight symbolic analysis provides a valuable tool for DNN validation.