Multi-objective metamorphic follow-up test case selection for deep learning systems

Deep Learning (DL) components are increasing their presence in safety and mission-critical software systems. To ensure a high dependability of DL systems, robust verification methods are required, for which automation is highly beneficial (e.g., more test cases can be executed). Metamorphic Testing (MT) is a technique that has shown to alleviate the test oracle problem when testing DL systems, and therefore, increasing test automation. However, a drawback of this technique lies into the need of multiple test executions to obtain the test verdict (named as the source and the follow-up test cases), requiring additional testing cost. In this paper we propose an approach based on multi-objective search to select follow-up test cases. Our approach makes use of source test cases to measure the uncertainty provoked by such test inputs in the DL model, and based on that, select failure-revealing follow-up test cases. We integrate our approach with the NSGA-II algorithm. An empirical evaluation on three DL models tackling the image classification problem, along with five different metamorphic relations demonstrates that our approach outperformed the baseline algorithm between 17.09 to 59.20% on average when considering the revisited Hypervolume quality indicator.