NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems

Abstract: 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 over-approximate 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.

• The paper introduces NNV as a verification tool that applies set-based reachability methods to analyze safety in deep neural networks and cyber-physical systems.
• It demonstrates a 20.7× speed improvement over Reluplex through the exact-star approach when verifying ACAS Xu properties.
• NNV’s advanced abstraction techniques reduce conservativeness, enabling scalable and precise verification of learning-enabled control systems.

The Neural Network Verification Tool: Advancements in DNN and CPS Verification

The paper presents a comprehensive overview of the Neural Network Verification (NNV) tool, which is designed to conduct set-based verification for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS), particularly focusing on neural network control systems (NNCS). This tool emerges as a pivotal asset for mitigating the complexities inherent in DNNs utilized in safety-critical applications, addressing safety and robustness verification challenges.

Core Functionality

NNV offers a range of reachability algorithms that employ various set representations—such as polyhedra, star sets, zonotopes, and abstract-domain representations—to evaluate the safety and robustness of feed-forward neural networks (FFNNs) and CNNs. For learning-enabled CPS that integrate DNNs, NNV provides both exact and over-approximate reachability methods catered specifically for systems with linear or nonlinear plant dynamics. This robust approach enables the application of NNV in diverse real-world contexts, such as safety verification of adaptive cruise control systems and air traffic collision avoidance networks.

Numerical and Experimental Insights

The paper reports compelling numerical results that highlight the efficacy of NNV in system verification tasks. It demonstrates significant improvements over other verification tools, such as Reluplex and Marabou, particularly in terms of verification speed and computational efficiency. For instance, the NNV's exact-star method is 20.7 times faster than Reluplex in verifying certain properties of ACAS Xu networks. Additionally, the approximate star method evidences markedly reduced conservativeness in safety verification, proving more networks safe compared to zonotopes and abstract domain methods.

Theoretical and Practical Implications

The theoretical construct of NNV leverages enhanced reachability algorithms that optimize computational processes by minimizing linear programming optimization requirements. This capability is pivotal in preventing the explosion of conservativeness experienced by traditional polyhedron methods, especially when verifying NNCS with linear plant models. Practically, NNV's capability for exact and over-approximate analysis facilitates robust and scalable verifications, which are vital for the development and integration of DNNs in safety-critical domains.

Future Directions

Advancements outlined in the paper suggest several prospective developments, including enhanced integration with real-time systems and further refinement of abstraction techniques to improve verification precision and scalability. The research anticipates augmentations in robustness through refining the star set reachability algorithms and enhancing the compatibility of NNV with diverse plant dynamics models. This trajectory points to future applications in increasingly complex DNN architectures and broader CPS contexts.

Overall, NNV stands as a crucial tool for researchers and practitioners in AI and CPS domains, providing state-of-the-art solutions for ensuring the safety and reliability of systems powered by advanced neural networks.