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Over the past decade, a number of hardware and software advances have conspired to thrust deep learning and neural networks to the forefront of computing. Deep learning has created a qualitative shift in our conception of what software is and what it can do: Every day we're seeing new applications of deep learning, from healthcare to art, and it feels like we're only scratching the surface of a universe of new possibilities. This book offers the first introduction of foundational ideas from automated verification as applied to deep neural networks and deep learning. It is divided into three parts: Part 1 defines neural networks as data-flow graphs of operators over real-valued inputs. Part 2 discusses constraint-based techniques for verification. Part 3 discusses abstraction-based techniques for verification. The book is a self-contained treatment of a topic that sits at the intersection of machine learning and formal verification. It can serve as an introduction to the field for first-year graduate students or senior undergraduates, even if they have not been exposed to deep learning or verification.

Introduction to Neural Network Verification: A New Beginning 2. Neural Networks as Graphs 3. Correctness Properties 4. Logics and Satisfiability 5. Encodings of Neural Networks 6. DPLL Modulo Theories 7. Neural Theory Solvers 8. Neural Interval Abstraction 9. Neural Zonotope Abstraction 10. Neural Polyhedron Abstraction 11. Verifying with Abstract Interpretation 12. Abstract Training of Neural Networks 13. The Challenges Ahead Acknowledgements References

Aws Albarghouthi

Published: 2021

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Over the past decade, a number of hardware and software advances have conspired to thrust deep learning and neural networks to the forefront of computing. Deep learning has created a qualitative shift in our conception of what software is and what it can do: Every day we’re seeing new applications of deep learning, from healthcare to art, and it feels like we’re only scratching the surface of a universe of new possibilities. This book offers the first introduction of foundational ideas from automated verification as applied to deep neural networks and deep learning. It is divided into three parts: Part 1 defines neural networks as data-flow graphs of operators over real-valued inputs. Part 2 discusses constraint-based techniques for verification. Part 3 discusses abstraction-based techniques for verification. The book is a self-contained treatment of a topic that sits at the intersection of machine learning and formal verification. It can serve as an introduction to the field for first-year graduate students or senior undergraduates, even if they have not been exposed to deep learning or verification.
Neural networks are members of a class of software that have the potential to enable intelligent computational systems capable of simulating characteristics of biological thinking and learning. Currently no standards exist to verify and validate neural network-based systems. NASA Independent Verification and Validation Facility has contracted the Institute for Scientific Research, Inc. to perform research on this topic and develop a comprehensive guide to performing V&V on adaptive systems, with emphasis on neural networks used in safety-critical or mission-critical applications. Methods and Procedures for the Verification and Validation of Artificial Neural Networks is the culmination of the first steps in that research. This volume introduces some of the more promising methods and techniques used for the verification and validation (V&V) of neural networks and adaptive systems. A comprehensive guide to performing V&V on neural network systems, aligned with the IEEE Standard for Software Verification and Validation, will follow this book.
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.
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.
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Neural networks have been widely used in many applications, such as image classification and understanding, language processing, and control of autonomous systems. These networks work by mapping inputs to outputs through a sequence of layers. At each layer, the input to that layer undergoes an affine transformation followed by a simple nonlinear transformation before being passed to the next layer. Neural networks are being used for increasingly important tasks, and in some cases, incorrect outputs can lead to costly consequences, hence validation of correctness at each layer is vital. The sheer size of the networks makes this not feasible using traditional methods. In this monograph, the authors survey a class of methods that are capable of formally verifying properties of deep neural networks. In doing so, they introduce a unified mathematical framework for verifying neural networks, classify existing methods under this framework, provide pedagogical implementations of existing methods, and compare those methods on a set of benchmark problems. Algorithms for Verifying Deep Neural Networks serves as a tutorial for students and professionals interested in this emerging field as well as a benchmark to facilitate the design of new verification algorithms.
This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency.
The combination of verifiable training and BaB based verifiers opens promising directions for more efficient and scalable neural network verification.