Deep learning (DL) has achieved remarkable progress over the past decade and been widely applied to many safety-critical applications. However, the robustness of DL systems recently receives great concerns, such as adversarial examples against computer vision systems, which could potentially result in severe consequences. Adopting testing techniques could help to evaluate the robustness of a DL system and therefore detect vulnerabilities at an early stage. The main challenge of testing such systems is that its runtime state space is too large: if we view each neuron as a runtime state for DL, then a DL system often contains massive states, rendering testing each state almost impossible. For traditional software, combinatorial testing (CT) is an effective testing technique to reduce the testing space while obtaining relatively high defect detection abilities. In this paper, we perform an exploratory study of CT on DL systems. We adapt the concept in CT and propose a set of coverage criteria for DL systems, as well as a CT coverage guided test generation technique. Our evaluation demonstrates that CT provides a promising avenue for testing DL systems. We further pose several open questions and interesting directions for combinatorial testing of DL systems.

Deep learning defines a new data-driven programming paradigm that constructs the internal system logic of a crafted neuron network through a set of training data. Deep learning (DL) has been widely adopted in many safety-critical scenarios. However, a plethora of studies have shown that the state-of-the-art DL systems suffer from various vulnerabilities which can lead to severe consequences when applied to real-world applications. Currently, the robustness of a DL system against adversarial attacks is usually measured by the accuracy of test data. Considering the limitation of accessible test data, good performance on test data can hardly guarantee the robustness and generality of DL systems. Different from traditional software systems which have clear and controllable logic and functionality, a DL system is trained with data and lacks thorough understanding. This makes it difficult for system analysis and defect detection, which could potentially hinder its real-world deployment without safety guarantees. In this paper, we propose DeepGauge, a comprehensive and multi-granularity testing criteria for DL systems, which renders a complete and multi-faceted portrayal of the testbed. The in-depth evaluation of our proposed testing criteria is demonstrated on two well-known datasets, five DL systems, with four state-of-the-art adversarial data generation techniques. The effectiveness of DeepGauge sheds light on the construction of robust DL systems.