Biblio

Current testing for Deep Neural Networks (DNNs) focuses on quantity of test cases but ignores diversity. To the best of our knowledge, DeepXplore is the first white-box framework for Deep Learning testing by triggering differential behaviors between multiple DNNs and increasing neuron coverage to improve diversity. Since it is based on multiple DNNs facing problems that (1) the framework is not friendly to a single DNN, (2) if incorrect predictions made by all DNNs simultaneously, DeepXplore cannot generate test cases. This paper presents Test4Deep, a white-box testing framework based on a single DNN. Test4Deep avoids mistakes of multiple DNNs by inducing inconsistencies between predicted labels of original inputs and that of generated test inputs. Meanwhile, Test4Deep improves neuron coverage to capture more diversity by attempting to activate more inactivated neurons. The proposed method was evaluated on three popular datasets with nine DNNs. Compared to DeepXplore, Test4Deep produced average 4.59% (maximum 10.49%) more test cases that all found errors and faults of DNNs. These test cases got 19.57% more diversity increment and 25.88% increment of neuron coverage. Test4Deep can further be used to improve the accuracy of DNNs by average up to 5.72% (maximum 7.0%).

Mutation analysis generates tests that distinguish variations, or mutants, of an artifact from the original. Mutation analysis is widely considered to be a powerful approach to testing, and hence is often used to evaluate other test criteria in terms of mutation score, which is the fraction of mutants that are killed by a test set. But mutation analysis is also known to provide large numbers of redundant mutants, and these mutants can inflate the mutation score. While mutation approaches broadly characterized as reduced mutation try to eliminate redundant mutants, the literature lacks a theoretical result that articulates just how many mutants are needed in any given situation. Hence, there is, at present, no way to characterize the contribution of, for example, a particular approach to reduced mutation with respect to any theoretical minimal set of mutants. This paper's contribution is to provide such a theoretical foundation for mutant set minimization. The central theoretical result of the paper shows how to minimize efficiently mutant sets with respect to a set of test cases. We evaluate our method with a widely-used benchmark.