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      Verification of Deep Convolutional Neural Networks Using ImageStars

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          Abstract

          Convolutional Neural Networks (CNN) have redefined state-of-the-art in many real-world applications, such as facial recognition, image classification, human pose estimation, and semantic segmentation. Despite their success, CNNs are vulnerable to adversarial attacks, where slight changes to their inputs may lead to sharp changes in their output in even well-trained networks. Set-based analysis methods can detect or prove the absence of bounded adversarial attacks, which can then be used to evaluate the effectiveness of neural network training methodology. Unfortunately, existing verification approaches have limited scalability in terms of the size of networks that can be analyzed. In this paper, we describe a set-based framework that successfully deals with real-world CNNs, such as VGG16 and VGG19, that have high accuracy on ImageNet. Our approach is based on a new set representation called the ImageStar, which enables efficient exact and over-approximative analysis of CNNs. ImageStars perform efficient set-based analysis by combining operations on concrete images with linear programming (LP). Our approach is implemented in a tool called NNV, and can verify the robustness of VGG networks with respect to a small set of input states, derived from adversarial attacks, such as the DeepFool attack. The experimental results show that our approach is less conservative and faster than existing zonotope and polytope methods.

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          Most cited references 9

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          Face recognition: a convolutional neural-network approach.

          We present a hybrid neural-network for human face recognition which compares favourably with other methods. The system combines local image sampling, a self-organizing map (SOM) neural network, and a convolutional neural network. The SOM provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the SOM, and a multilayer perceptron (MLP) in place of the convolutional network for comparison. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze the computational complexity and discuss how new classes could be added to the trained recognizer.
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            Output Reachable Set Estimation and Verification for Multilayer Neural Networks

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              Reluplex: an efficient SMT solver for verifying deep neural networks

               G. KATZ,  C. BARRETT,  DL Dill (2017)
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                Author and article information

                Contributors
                shuvendu.lahiri@microsoft.com
                wang626@usc.edu
                taylor.johnson@vanderbilt.edu
                Journal
                978-3-030-53288-8
                10.1007/978-3-030-53288-8
                Computer Aided Verification
                Computer Aided Verification
                32nd International Conference, CAV 2020, Los Angeles, CA, USA, July 21–24, 2020, Proceedings, Part I
                978-3-030-53287-1
                978-3-030-53288-8
                13 June 2020
                13 June 2020
                : 12224
                : 18-42
                Affiliations
                [8 ]GRID grid.419815.0, ISNI 0000 0001 2181 3404, Microsoft Research Lab, ; Redmond, WA USA
                [9 ]GRID grid.42505.36, ISNI 0000 0001 2156 6853, University of Southern California, ; Los Angeles, CA USA
                [10 ]GRID grid.24434.35, ISNI 0000 0004 1937 0060, University of Nebraska, ; Lincoln, USA
                [11 ]GRID grid.152326.1, ISNI 0000 0001 2264 7217, Vanderbilt University, ; Nashville, USA
                [12 ]GRID grid.36425.36, ISNI 0000 0001 2216 9681, Stony Brook University, ; Stony Brook, USA
                [13 ]GRID grid.410427.4, ISNI 0000 0001 2284 9329, Augusta University, ; Augusta, USA
                Article
                2
                10.1007/978-3-030-53288-8_2
                7363231
                © The Author(s) 2020

                Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

                The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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                © The Editor(s) (if applicable) and The Author(s) 2020
                Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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