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.

Highlights

  • Deep neural networks (DNNs) have quickly become one of the most widely used tools for dealing with complex and challenging problems in numerous domains, such as image classification [10,16,25], function approximation, and natural language translation [11,18]

  • Neural Network Verification (NNV) provides a set of reachability algorithms that can compute both the exact and over-approximate reachable sets of DNNs and neural network control systems (NNCS) using a variety of set representations such as polyhedra [40,53–56], star sets [29,38,39,41], zonotopes [32], and abstract domain representations [33]

  • NNV can compute both the exact and over-approximate reachable sets of the adaptive cruise control (ACC) system in bounded time steps, while for nonlinear dynamics, NNV constructs an over-approximation of the reachable sets

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Summary

Introduction

Deep neural networks (DNNs) have quickly become one of the most widely used tools for dealing with complex and challenging problems in numerous domains, such as image classification [10,16,25], function approximation, and natural language translation [11,18]. Components Plant dynamics (for NNCS) Discrete/Continuous (for NNCS) Activation functions CNN Layers Reachability methods Reachable set/Flow-pipe Visualization Parallel computing Safety verification Falsification Robustness verification (for FFNN/CNN) Counterexample generation. ReLU, Satlin, Sigmoid, Tanh MaxPool, Conv, BN, AvgPool, FC Star, Zonotope, Abstract-domain, ImageStar Yes. NNV can construct a complete set of counter-examples demonstrating the set of all possible unsafe initial inputs and states by using the star-based exact reachability algorithm [38,41]. NNV has been successfully applied to safety verification and robustness analysis of several real-world DNNs, primarily feedforward neural networks (FFNNs) and convolutional neural networks (CNNs), as well as learning-enabled CPS. The first compares methods for safety verification of the ACAS Xu networks [21], and the second presents safety verification of a learning-based adaptive cruise control (ACC) system

Overview and Features
Set Representations and Reachability Algorithms
Star Set [38, 41] (code)
Zonotope [32] (code)
ImageStar Set [37] (code)
Safety Verification of ACAS Xu Networks
Safety Verification of Adaptive Cruise Control System
Related Work
Conclusions
Full Text
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