This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports overapproximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks, and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

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This paper introduces robustness verification for semantic segmentation neural networks (in short, semantic segmentation networks [SSNs]), building on and extending recent approaches for robustness verification of image classification neural networks. Despite recent progress in developing verification methods for specifications such as local adversarial robustness in deep neural networks (DNNs) in terms of scalability, precision, and applicability to different network architectures, layers, and activation functions, robustness verification of semantic segmentation has not yet been considered. We address this limitation by developing and applying new robustness analysis methods for several segmentation neural network architectures, specifically by addressing reachability analysis of up-sampling layers, such as transposed convolution and dilated convolution. We consider several definitions of robustness for segmentation, such as the percentage of pixels in the output that can be proven robust under different adversarial perturbations, and a robust variant of intersection-over-union (IoU), the typical performance evaluation measure for segmentation tasks. Our approach is based on a new relaxed reachability method, allowing users to select the percentage of a number of linear programming problems (LPs) to solve when constructing the reachable set, through a relaxation factor percentage. The approach is implemented within NNV, then applied and evaluated on segmentation datasets, such as a multi-digit variant of MNIST known as M2NIST. Thorough experiments show that by using transposed convolution for up-sampling and average-pooling for down-sampling, combined with minimizing the number of ReLU layers in the SSNs, we can obtain SSNs with not only high accuracy (IoU), but also that are more robust to adversarial attacks and amenable to verification. Additionally, using our new relaxed reachability method, we can significantly reduce the verification time for neural networks whose ReLU layers dominate the total analysis time, even in classification tasks.

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Neural networks have been widely used to solve complex realworld problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the behaviors of neural network systems will be crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural network involved in the model is a class of feed-forward neural networks called Multi-Layer Perceptron (MLP). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation for each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of intersections of unsafe regions and estimated reachable set.Several numerical examples are provided to illustrate our approach.

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2021. In the third edition of this AINNCS category at ARCH-COMP, three tools have been applied to solve seven different benchmark problems, (in alphabetical order): JuliaReach, NNV, and Verisig. JuliaReach is a new participant in this category, Verisig participated previously in 2019 and NNV has participated in all previous competitions. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results combined with 2020 results probably provide the most complete assessment of current tools for safety verification of NNCS.

Verification has emerged as a means to provide formal guarantees on learning-based systems incorporating neural network before using them in safety-critical applications. This paper proposes a new verification approach for deep neural networks (DNNs) with piecewise linear activation functions using reachability analysis. The core of our approach is a collection of reachability algorithms using star sets (or shortly, stars), an effective symbolic representation of high-dimensional polytopes. The star-based reachability algorithms compute the output reachable sets of a network with a given input set before using them for verification. For a neural network with piecewise linear activation functions, our approach can construct both exact and over-approximate reachable sets of the neural network. To enhance the scalability of our approach, a star set is equipped with an outer-zonotope (a zonotope over-approximation of the star set) to quickly estimate the lower and upper bounds of an input set at a specific neuron to determine if splitting occurs at that neuron. This zonotope pre-filtering step reduces significantly the number of linear programming optimization problems that must be solved in the analysis, and leads to a reduction in computation time, which enhances the scalability of the star set approach. Our reachability algorithms are implemented in a software prototype called the neural network verification tool, and can be applied to problems analyzing the robustness of machine learning methods, such as safety and robustness verification of DNNs. Our experiments show that our approach can achieve runtimes twenty to 1400 times faster than Reluplex, a satisfiability modulo theory-based approach. Our star set approach is also less conservative than other recent zonotope and abstract domain approaches.

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. In the second edition of this AINNCS category at ARCH-COMP, four tools have been applied to solve seven different benchmark problems, (in alphabetical order): NNV, OVERT, ReachNN*, and VenMAS. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results probably provide the most complete assessment of current tools for safety verification of NNCS.