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.

本文介绍神经网络验证（NNV）软件工具，该工具为深度神经网络（DNN）和学习启用的控制系统（CPS）提供了一套基于集合的验证框架。NNV 的核心是一组可达性算法，这些算法利用了多种集合表示，例如，多面体、恒星集、zono topes 和抽象域表示。