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The combination of verifiable training and BaB based verifiers opens promising directions for more efficient and scalable neural network verification.
Deep neural networks have achieved great success on many tasks and even surpass human performance in certain settings. Despite this success, neural networks are known to be vulnerable to the problem of adversarial inputs, where small and human- imperceptible changes in the input cause large and unexpected changes in the output. This problem motivates the development of neural network verification techniques that aspire to verify that a given neural network produces stable predictions for all inputs in a perturbation space around a given input. However, many existing verifiers target floating point networks but, for efficiency reasons, do not exactly model the floating point computation. As a result, they may produce incorrect results due to floating point error. In this context, Binarized Neural Networks (BNNs) are attractive because they work with quantized inputs and binarized internal activation and weight values and thus support verification free of floating point error. The binarized computation of BNNs directly corresponds to logical reasoning. BNN verification is, therefore, typically formulated as a Boolean satisfiability (SAT) problem. This formulation involves numerous reified cardinality constraints. Previous work typically converts such constraints to conjunctive normal form to be solved by an off-the-shelf SAT solver. Unfortunately, previous BNN verifiers are significantly slower than floating point network verifiers. Moreover, there is a dearth of prior research that aspires to train robust BNNs. This thesis presents techniques for ensuring neural network robustness against input perturbations and checking safety properties that require a network to produce certain outputs for a set of inputs. We present four contributions: (i) new techniques that improve BNN verification performance by thousands of times compared to the best previous verifiers for either binarized or floating point neural networks; (ii) the first technique for training robust BNNs; previous robust training techniques are designed to work with floating point networks and do not produce robust BNNs; (iii) a new method that exploits floating point errors to produce witnesses for the unsoundness of verifiers that target floating point networks but do not exactly model 3floating point arithmetic; and (iv) a new technique for efficient and exact verification of neural networks with low dimensional inputs. Our first contribution comprises two novel techniques to improve BNN verification performance: (i) extending the SAT solver to handle reified cardinality constraints natively and efficiently; and (ii) novel training strategies that produce BNNs that verify more efficiently. Our second contribution is a new training technique for training BNNs that achieve verifiable robustness comparable to floating point networks. We present an algorithm that adaptively tunes the gradient computation in PGD-based BNN adversarial train- ing to improve the robustness. We demonstrate the effectiveness of the methods in the first two contributions by presenting the first exact verification results for adversarial robustness of nontrivial convolutional BNNs on the widely used MNIST and CIFAR10 datasets. No previous BNN verifiers can handle these tasks. Compared to previous (potentially incorrect) exact verification of floating point networks of the same architectures on the same tasks, our system verifies BNNs hundreds to thousands of times faster and delivers comparable verifiable accuracy in most cases. Our third contribution shows that the failure to take floating point error into ac- count leads to incorrect verification that can be systematically exploited. We present a method that efficiently searches inputs as witnesses for the incorrectness of robust- ness claims made by a complete verifier regarding a pretrained neural network. We also show that it is possible to craft neural network architectures and weights that cause an unsound incomplete verifier to produce incorrect verification results. Our fourth contribution shows that the idea of quantization also facilitates the verification of floating point networks. Specifically, we consider exactly verifying safety properties for floating point neural networks used for a low dimensional airborne avoidance control system. Prior work, which analyzes the internal computations of the network, is inefficient and potentially incorrect because it does not soundly model floating point arithmetic. We instead prepend an input quantization layer to the original network. Our experiments show that our modification delivers similar runtime accuracy while allowing correct and significantly easier and faster verification by input state space enumeration.
This open access two-volume set LNCS 12759 and 12760 constitutes the refereed proceedings of the 33rd International Conference on Computer Aided Verification, CAV 2021, held virtually in July 2021. The 63 full papers presented together with 16 tool papers and 5 invited papers were carefully reviewed and selected from 290 submissions. The papers were organized in the following topical sections: Part I: invited papers; AI verification; concurrency and blockchain; hybrid and cyber-physical systems; security; and synthesis. Part II: complexity and termination; decision procedures and solvers; hardware and model checking; logical foundations; and software verification. This is an open access book.
This book presents the proceedings of the 24th European Conference on Artificial Intelligence (ECAI 2020), held in Santiago de Compostela, Spain, from 29 August to 8 September 2020. The conference was postponed from June, and much of it conducted online due to the COVID-19 restrictions. The conference is one of the principal occasions for researchers and practitioners of AI to meet and discuss the latest trends and challenges in all fields of AI and to demonstrate innovative applications and uses of advanced AI technology. The book also includes the proceedings of the 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020) held at the same time. A record number of more than 1,700 submissions was received for ECAI 2020, of which 1,443 were reviewed. Of these, 361 full-papers and 36 highlight papers were accepted (an acceptance rate of 25% for full-papers and 45% for highlight papers). The book is divided into three sections: ECAI full papers; ECAI highlight papers; and PAIS papers. The topics of these papers cover all aspects of AI, including Agent-based and Multi-agent Systems; Computational Intelligence; Constraints and Satisfiability; Games and Virtual Environments; Heuristic Search; Human Aspects in AI; Information Retrieval and Filtering; Knowledge Representation and Reasoning; Machine Learning; Multidisciplinary Topics and Applications; Natural Language Processing; Planning and Scheduling; Robotics; Safe, Explainable, and Trustworthy AI; Semantic Technologies; Uncertainty in AI; and Vision. The book will be of interest to all those whose work involves the use of AI technology.
Machine learning has proven useful in a wide variety of domains from computer vision to control of autonomous systems. However, if we want to use neural networks in safety critical systems such as vehicles and aircraft, we need reliability guarantees. We turn to formal methods to verify that neural networks do not have unexpected behavior, such as misclassifying an image after a small amount of random noise is added. Within formal methods, there is a small but growing body of work focused on neural network verification. However, most of this work only reasons about neural networks in isolation, when in reality, neural networks are often used within large, complex systems. We build on this literature to verify neural networks operating within nonlinear systems. Our first contribution is to enable the use of mixed-integer linear programming for verification of systems containing both ReLU neural networks and smooth nonlinear functions. Mixed-integer linear programming is a common tool used for verifying neural networks with ReLU activation functions, and while effective, does not natively permit the use of nonlinear functions. We introduce an algorithm to overapproximate arbitrary nonlinear functions using piecewise linear constraints. These piecewise linear constraints can be encoded into a mixed-integer linear program, allowing verification of systems containing both ReLU neural networks and nonlinear functions. We use a special kind of approximation known as overapproximation which allows us to make sound claims about the original nonlinear system when we verify the overapproximate system. The next two contributions of this thesis are to apply the overapproximation algorithm to two different neural network verification settings: verifying inverse model neural networks and verifying neural network control policies. Frequently appearing in a variety of domains from medical imaging to state estimation, inverse problems involve reconstructing an underlying state from observations. The model mapping states to observations can be nonlinear and stochastic, making the inverse problem difficult. Neural networks are ideal candidates for solving inverse problems because they are very flexible and can be trained from data. However, inverse model neural networks lack built-in accuracy guarantees. We introduce a method to solve for verified upper bounds on the error of an inverse model neural network. The next verification setting we address is verifying neural network control policies for nonlinear dynamical systems. A control policy directs a dynamical system to perform a desired task such as moving to a target location. When a dynamical system is highly nonlinear and difficult to control, traditional control approaches may become computationally intractable. In contrast, neural network control policies are fast to execute. However, neural network control policies lack the stability, safety, and convergence guarantees that are often available to more traditional control approaches. In order to assess the safety and performance of neural network control policies, we introduce a method to perform finite time reachability analysis. Reachability analysis reasons about the set of states reachable by the dynamical system over time and whether that set of states is unsafe or is guaranteed to reach a goal. The final contribution of this thesis is the release of three open source software packages implementing methods described herein. The field of formal verification for neural networks is small and the release of open source software will allow it to grow more quickly as it makes iteration upon prior work easier. Overall, this thesis contributes ideas, methods, and tools to build confidence in deep learning systems. This area will continue to grow in importance as deep learning continues to find new applications.
This book provides guidance on the verification and validation of neural networks/adaptive systems. Considering every process, activity, and task in the lifecycle, it supplies methods and techniques that will help the developer or V&V practitioner be confident that they are supplying an adaptive/neural network system that will perform as intended. Additionally, it is structured to be used as a cross-reference to the IEEE 1012 standard.
Neural Networks and their implementation decoded with TensorFlowAbout This Book* Develop a strong background in neural network programming from scratch, using the popular Tensorflow library.* Use Tensorflow to implement different kinds of neural networks - from simple feedforward neural networks to multilayered perceptrons, CNNs, RNNs and more.* A highly practical guide including real-world datasets and use-cases to simplify your understanding of neural networks and their implementation.Who This Book Is ForThis book is meant for developers with a statistical background who want to work with neural networks. Though we will be using TensorFlow as the underlying library for neural networks, book can be used as a generic resource to bridge the gap between the math and the implementation of deep learning. If you have some understanding of Tensorflow and Python and want to learn what happens at a level lower than the plain API syntax, this book is for you.What You Will Learn* Learn Linear Algebra and mathematics behind neural network.* Dive deep into Neural networks from the basic to advanced concepts like CNN, RNN Deep Belief Networks, Deep Feedforward Networks.* Explore Optimization techniques for solving problems like Local minima, Global minima, Saddle points* Learn through real world examples like Sentiment Analysis.* Train different types of generative models and explore autoencoders.* Explore TensorFlow as an example of deep learning implementation.In DetailIf you're aware of the buzz surrounding the terms such as "machine learning," "artificial intelligence," or "deep learning," you might know what neural networks are. Ever wondered how they help in solving complex computational problem efficiently, or how to train efficient neural networks? This book will teach you just that.You will start by getting a quick overview of the popular TensorFlow library and how it is used to train different neural networks. You will get a thorough understanding of the fundamentals and basic math for neural networks and why TensorFlow is a popular choice Then, you will proceed to implement a simple feed forward neural network. Next you will master optimization techniques and algorithms for neural networks using TensorFlow. Further, you will learn to implement some more complex types of neural networks such as convolutional neural networks, recurrent neural networks, and Deep Belief Networks. In the course of the book, you will be working on real-world datasets to get a hands-on understanding of neural network programming. You will also get to train generative models and will learn the applications of autoencoders.By the end of this book, you will have a fair understanding of how you can leverage the power of TensorFlow to train neural networks of varying complexities, without any hassle. While you are learning about various neural network implementations you will learn the underlying mathematics and linear algebra and how they map to the appropriate TensorFlow constructs.Style and ApproachThis book is designed to give you just the right number of concepts to back up the examples. With real-world use cases and problems solved, this book is a handy guide for you. Each concept is backed by a generic and real-world problem, followed by a variation, making you independent and able to solve any problem with neural networks. All of the content is demystified by a simple and straightforward approach.