Using Quantifier Elimination to Enhance the Safety Assurance of Deep Neural Networks

TL;DR

This paper explores using quantifier elimination, a formal mathematical technique, to improve safety verification of deep neural networks, demonstrated on an airborne collision avoidance system.

Contribution

It introduces quantifier elimination as a new formal method tool for DNN safety assurance, complementing existing static analysis techniques.

Findings

Successfully formulated DNN robustness analysis using QE

Applied QE to an airborne collision avoidance DNN

Initial results show promise for formal safety verification

Abstract

Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems hinders their real-world adoption in safety-critical domains such as aerospace and medical devices. Hence, there is a surge in interest to explore the use of advanced mathematical techniques such as formal methods to address this challenge. In fact, the initial results of such efforts are promising. Along these lines, we propose the use of quantifier elimination (QE) - a formal method technique, as a complimentary technique to the state-of-the-art static analysis and verification procedures. Using an airborne collision avoidance DNN as a case example, we illustrate the use of QE to formulate the precise range forward propagation through a network as well as analyze its robustness. We discuss the initial results of this ongoing work and explore the future possibilities of extending this approach and/or integrating it with other approaches to perform advanced safety assurance of DNNs.