The robustness of neural network classifiers is important in the safety-critical domain and can be quantified by robustness verification. At present, efficient and scalable verification techniques are always sound but incomplete, and thus, the improvement of verified robustness results is the key criterion to evaluate the performance of incomplete verification approaches. The multi-variate function MaxPool is widely adopted yet challenging to verify. In this paper, we present Ti-Lin, a robustness verifier for MaxPool-based CNNs with Tight Linear Approximation. Following the sequel of minimizing the over-approximation zone of the nonlinear function of CNNs, we are the first to propose the provably neuron-wise tightest linear bounds for the MaxPool function. By our proposed linear bounds, we can certify larger robustness results for CNNs. We evaluate the effectiveness of Ti-Lin on different verification frameworks with open-sourced benchmarks, including LeNet, PointNet, and networks trained on the MNIST, CIFAR-10, Tiny ImageNet and ModelNet40 datasets. Experimental results show that Ti-Lin significantly outperforms the state-of-the-art methods across all networks with up to 78.6% improvement in terms of the certified accuracy with almost the same time consumption as the fastest tool. Our code is available at https://github.com/xiaoyuanpigo/Ti-Lin-Hybrid-Lin.

Convolutional Neural Network (CNN) operators, mostly based on mathematical linear computations, are of vital importance to developing CNN-based software. Existing studies reveal that these operators are prone to floating-point precision problems (FPPs). In a CNN-based application, such problems can be propagated and result in catastrophic consequences. Thus, it is highly desired to detect and repair the FPPs in CNN operators. Considering the FPPs in CNN operators are mainly caused by accumulated floating-point errors and diverse floating-point tensors instead of wrong codes or bad implementations, it requires much time cost and is difficult to tackle these FPPs. In this paper, we propose the first method for the automated detection and repair of FPPs in CNN operators from the perspective of floating-point tensors. To generate diverse tensors with floating-point numbers, we design two levels of mutation rules, namely computation-level mutation and input-level mutation, containing a total of five mutation methods. To detect the FPPs caused by the accumulated floating-point errors, our method uses a weight matrix to guide the progressive mutation. To repair the detected FPPs, our method transforms the error-prone floating-point tensors based on the mathematical rewriting of the floating-point linear computational properties without destroying the original computation. Experimental results show that our methods can detect and repair FPPs in CNN operators effectively and efficiently and could reduce 93.32% to 100% of the FPPs in CNN operators. We conduct a case study on six different widely-used CNN models and confirm that the proposed FPP method is generalizable and effective across a variety of tasks and architectures. Our detection and repair method offers an intuitive way to handle FPPs during development, allowing users to continue building and fine-tuning their models without being slowed down by numerical precision errors. We believe that our method could open up a new way to enhance the quality of CNN operators and CNN-based software.

Deep learning (DL) libraries have become the key component in developing and deploying DL-based software nowadays. With the growing popularity of applying DL models in both academia and industry across various domains, any bugs inherent in the DL libraries can potentially cause unexpected server outcomes. As such, there is an urgent demand for improving the software quality of DL libraries. Although there are some existing approaches specifically designed for testing DL libraries, their focus is usually limited to one specific domain, such as computer vision (CV). It is still not very clear how the existing approaches perform in detecting bugs of different DL libraries regarding different task domains and to what extent. To bridge this gap, we first conduct an empirical study on four representative and state-of-the-art DL library testing approaches. Our empirical study results reveal that it is hard for existing approaches to generalize to other task domains. We also find that the test inputs generated by these approaches usually lack diversity, with only a few types of bugs. What is worse, the false-positive rate of existing approaches is also high ( up to 58% ). To address these issues, we propose a guided differential fuzzing approach based on generation , namely, Gandalf . To generate testing inputs across diverse task domains effectively, Gandalf adopts the context-free grammar to ensure validity and utilizes a Deep Q-Network to maximize the diversity. Gandalf also includes 15 metamorphic relations to make it possible for the generated test cases to generalize across different DL libraries. Such a design can decrease the false positives because of the semantic difference for different APIs. We evaluate the effectiveness of Gandalf on nine versions of three representative DL libraries, covering 309 operators from computer vision, natural language processing, and automated speech recognition. The evaluation results demonstrate that Gandalf can effectively and efficiently generate diverse test inputs. Meanwhile, Gandalf successfully detects five categories of bugs with only 3.1% false-positive rates. We report all 49 new unique bugs found during the evaluation to the DL libraries’ developers, and most of these bugs have been confirmed. Details about our empirical study and evaluation results are available on our project website. 1