Markov model based coverage testing of deep learning software systems

Context: Deep Learning (DL) software systems have been widely deployed in safety and security-critical domains, which calls for systematic testing to guarantee their accuracy and reliability. Objective measurement of test quality is one of the key issues in software testing. Recently, many coverage criteria have been proposed to measure the testing adequacy of Deep Neural Networks (DNNs). Objective: Recent research demonstrates that existing criteria have some limitations on interpreting the increasingly diverse behaviors of DNNs or clarifying the relationship between the coverage and the decision logic of DNNs. Moreover, some evaluations argue against the correlation between coverage and defect detection. In this paper, a novel coverage approach is proposed to interpret the internal information of programs. Methods: The process of coverage testing is formalized and quantified by constructing Markov models based on critical neurons extracted using Layer-wise Relevance Propagation in the structure of DNNs. The difference in the transition matrix of Markov chains between training and testing data is measured by KL divergence, and it is developed as a coverage criterion. Results: The values of the proposed coverage increase as the number of classes increases. The values are different for various test suites, and they become higher with the addition of new samples. Higher coverage values are observed to correlate with an increased fault detection capability. Conclusion: The experimental results illustrate that the proposed approach can effectively measure actual diversity and exhibit more adaptability to additional test cases. Furthermore, there is a positive correlation between the proposed coverage and fault detection, which provides support for test case selection guided by coverage.