Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations
Abstract
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed to compute output reachable set. The computation is formulated in the form of a set of manipulations for a union of polyhedra, which can be efficiently applied with the aid of polyhedron computation tools. Based on the output reachable set computation results, the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra. A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper.
Keywords
Cite
@article{arxiv.1712.08163,
title = {Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations},
author = {Weiming Xiang and Hoang-Dung Tran and Taylor T. Johnson},
journal= {arXiv preprint arXiv:1712.08163},
year = {2017}
}