Scaling Model Checking for Neural Network Analysis via State-Space Reduction and Input Segmentation

Abstract

Owing to their remarkable learning capabilities and performance in real-world applica- tions, the use of machine learning systems based on Deep Neural Networks (DNNs) has been continuously increasing. However, various case studies and empirical findings in the literature suggest that slight variations to DNN inputs can lead to erroneous and undesir- able DNN behavior. This has led to considerable interest in their formal analysis, aiming to provide guarantees regarding a given DNN’s behavior. Existing frameworks provide robust- ness and/or safety guarantees for the trained DNNs, using satisfiability solving and linear programming. We proposed FANNet, the first model checking-based framework for analyz- ing a broader range of DNN properties. However, the state-space explosion associated with model checking entails a scalability problem, making the FANNet applicable only to small DNNs. This work develops state-space reduction and input segmentation approaches, to improve the scalability and timing efficiency of formal DNN analysis. Compared to the state-of-the-art FANNet, this enables our new model checking-based framework to reduce the verification’s timing overhead by a factor of up to 8000, making the framework ap- plicable to DNNs even with approximately 80 times more network parameters. This in turn allows the analysis of DNN safety properties using the new framework, in addition to all the DNN properties already included with FANNet. The framework is shown to be efficiently able to analyze properties of DNNs trained on healthcare datasets as well as the well-acknowledged ACAS Xu networks.