723 research outputs found
An Abstraction-Based Framework for Neural Network Verification
Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network verification approaches have recently been proposed. However, these approaches afford limited scalability, and applying them to large networks can be challenging. In this paper, we propose a framework that can enhance neural network verification techniques by using over-approximation to reduce the size of the network—thus making it more amenable to verification. We perform the approximation such that if the property holds for the smaller (abstract) network, it holds for the original as well. The over-approximation may be too coarse, in which case the underlying verification tool might return a spurious counterexample. Under such conditions, we perform counterexample-guided refinement to adjust the approximation, and then repeat the process. Our approach is orthogonal to, and can be integrated with, many existing verification techniques. For evaluation purposes, we integrate it with the recently proposed Marabou framework, and observe a significant improvement in Marabou’s performance. Our experiments demonstrate the great potential of our approach for verifying larger neural networks
Formal Verification of Neural Network Controlled Autonomous Systems
In this paper, we consider the problem of formally verifying the safety of an
autonomous robot equipped with a Neural Network (NN) controller that processes
LiDAR images to produce control actions. Given a workspace that is
characterized by a set of polytopic obstacles, our objective is to compute the
set of safe initial conditions such that a robot trajectory starting from these
initial conditions is guaranteed to avoid the obstacles. Our approach is to
construct a finite state abstraction of the system and use standard
reachability analysis over the finite state abstraction to compute the set of
the safe initial states. The first technical problem in computing the finite
state abstraction is to mathematically model the imaging function that maps the
robot position to the LiDAR image. To that end, we introduce the notion of
imaging-adapted sets as partitions of the workspace in which the imaging
function is guaranteed to be affine. We develop a polynomial-time algorithm to
partition the workspace into imaging-adapted sets along with computing the
corresponding affine imaging functions. Given this workspace partitioning, a
discrete-time linear dynamics of the robot, and a pre-trained NN controller
with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge
is to analyze the behavior of the neural network. To that end, we utilize a
Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible
segments of different ReLUs. SMC solvers then use a Boolean satisfiability
solver and a convex programming solver and decompose the problem into smaller
subproblems. To accelerate this process, we develop a pre-processing algorithm
that could rapidly prune the space feasible ReLU segments. Finally, we
demonstrate the efficiency of the proposed algorithms using numerical
simulations with increasing complexity of the neural network controller
Work In Progress: Safety and Robustness Verification of Autoencoder-Based Regression Models using the NNV Tool
This work in progress paper introduces robustness verification for
autoencoder-based regression neural network (NN) models, following
state-of-the-art approaches for robustness verification of image classification
NNs. Despite the ongoing progress in developing verification methods for safety
and robustness in various deep neural networks (DNNs), robustness checking of
autoencoder models has not yet been considered. We explore this open space of
research and check ways to bridge the gap between existing DNN verification
methods by extending existing robustness analysis methods for such autoencoder
networks. While classification models using autoencoders work more or less
similar to image classification NNs, the functionality of regression models is
distinctly different. We introduce two definitions of robustness evaluation
metrics for autoencoder-based regression models, specifically the percentage
robustness and un-robustness grade. We also modified the existing Imagestar
approach, adjusting the variables to take care of the specific input types for
regression networks. The approach is implemented as an extension of NNV, then
applied and evaluated on a dataset, with a case study experiment shown using
the same dataset. As per the authors' understanding, this work in progress
paper is the first to show possible reachability analysis of autoencoder-based
NNs.Comment: In Proceedings SNR 2021, arXiv:2207.0439
- …