Deep learning (DL) libraries have become increasingly popular and their quality assurance is also gaining significant attention. Although many fault detection techniques have been proposed, effective fault localization techniques tailored to DL libraries are scarce. Due to the unique characteristics of DL libraries (e.g., complicated code architecture supporting DL model training and inference with extensive multidimensional tensor calculations), the effectiveness of existing fault localization techniques for traditional software is also unknown on DL library faults. To bridge this gap, we conducted the first empirical study to investigate the effectiveness of fault localization on DL libraries. Specifically, we evaluated spectrum-based fault localization (SBFL) due to its high generalizability and affordable overhead on such complicated libraries. Based on the key aspects in SBFL, our study investigated the effectiveness of SBFL with different sources of passing test cases (including human-written, fuzzer-generated, and mutation-based test cases) and various suspicious value calculation methods. In particular, mutation-based test cases are produced by our designed rule-based mutation technique and LLM-based mutation technique tailored to DL library faults. To enable our extensive study, we built the first benchmark (Defects4DLL), which contains 120 real-world faults in PyTorch and TensorFlow with easy-to-use experimental environments. Our study delivered a series of useful findings. For example, the rule-based approach is effective in localizing crash faults in DL libraries, successfully localizing 44.44% of crash faults within Top-10 functions and 74.07% of crash faults within Top-10 files, while the passing test cases from DL library fuzzers perform poorly on this task. Furthermore, based on our findings on the complementarity of different sources, we designed a hybrid technique by effectively integrating human-written, LLM-mutated, rule-based mutated test cases, which further achieves 31.48%$\boldsymbol{\sim}$61.36% improvements over each single source in terms of the number of detected faults within Top-5 files.

Abstract Many test coverage metrics have been proposed to measure the deep neural network (DNN) testing effectiveness, including structural coverage and nonstructural coverage. These test coverage metrics are proposed based on the fundamental assumption: They are correlated with test effectiveness. However, the fundamental assumption is still not validated sufficiently and reasonably, which brings question on the usefulness of DNN test coverage. This paper conducted a revisiting study on the existing DNN test coverage from the test effectiveness perspective, to effectively validate the fundamental assumption. Here, we carefully considered the diversity of subjects, three test effectiveness criteria, and both typical and state‐of‐the‐art test coverage metrics. Different from all the existing studies that deliver negative conclusions on the usefulness of existing DNN test coverage, we identified some positive conclusions on their usefulness from the test effectiveness perspective. In particular, we found the complementary relationship between structural and nonstructural coverage and identified the practical usage scenarios and promising research directions for these existing test coverage metrics.

The task of a deep learning (DL) program is to train a model with high precision and apply it to different scenarios. A DL program often involves massive numerical calculations. Therefore, the robustness and stability of the numerical calculations are dominant in the quality of DL programs. Indeed, numerical bugs are common in DL programs, producing NaN (Not-a-Number) and INF (Infinite). A numerical bug may render the DL models inaccurate, causing the DL applications unusable. In this work, we conduct the first empirical study on numerical bugs in DL programs by analyzing the programs implemented on the top of two popular DL libraries (i.e., TensorFlow and PyTorch). Specifically, We collect a dataset of 400 numerical bugs in DL programs. Then, we classify these numerical bugs into nine categories based on their root causes and summarize two findings. Finally, we provide the implications of our study on detecting numerical bugs in DL programs.

Numerical computation is dominant in deep learning (DL) programs. Consequently, numerical bugs are one of the most prominent kinds of defects in DL programs. Numerical bugs can lead to exceptional values such as NaN (Not-a-Number) and INF (Infinite), which can be propagated and eventually cause crashes or invalid outputs. They occur when special inputs cause invalid parameter values at internal mathematical operations such as log(). In this paper, we propose the first dynamic technique, called GRIST, which automatically generates a small input that can expose numerical bugs in DL programs. GRIST piggy-backs on the built-in gradient computation functionalities of DL infrastructures. Our evaluation on 63 real-world DL programs shows that GRIST detects 78 bugs including 56 unknown bugs. By submitting them to the corresponding issue repositories, eight bugs have been confirmed and three bugs have been fixed. Moreover, GRIST can save 8.79X execution time to expose numerical bugs compared to running original programs with its provided inputs. Compared to the state-of-the-art technique DEBAR (which is a static technique), DEBAR produces 12 false positives and misses 31 true bugs (of which 30 bugs can be found by GRIST), while GRIST only misses one known bug in those programs and no false positive. The results demonstrate the effectiveness of GRIST.

Deep learning (DL) techniques are rapidly developed and have been widely adopted in practice. However, similar to traditional software systems, DL systems also contain bugs, which could cause serious impacts especially in safety-critical domains. Recently, many research approaches have focused on testing DL models, while little attention has been paid for testing DL libraries, which is the basis of building DL models and directly affects the behavior of DL systems. In this work, we propose a novel approach, LEMON, to testing DL libraries. In particular, we (1) design a series of mutation rules for DL models, with the purpose of exploring different invoking sequences of library code and hard-to-trigger behaviors; and (2) propose a heuristic strategy to guide the model generation process towards the direction of amplifying the inconsistent degrees of the inconsistencies between different DL libraries caused by bugs, so as to mitigate the impact of potential noise introduced by uncertain factors in DL libraries. We conducted an empirical study to evaluate the effectiveness of LEMON with 20 release versions of 4 widely-used DL libraries, i.e., TensorFlow, Theano, CNTK, MXNet. The results demonstrate that LEMON detected 24 new bugs in the latest release versions of these libraries, where 7 bugs have been confirmed and one bug has been fixed by developers. Besides, the results confirm that the heuristic strategy for model generation indeed effectively guides LEMON in amplifying the inconsistent degrees for bugs.

Deep neural network (DNN) has become increasingly popular and DNN testing is very critical to guarantee the correctness of DNN, i.e., the accuracy of DNN in this work. However, DNN testing suffers from a serious efficiency problem, i.e., it is costly to label each test input to know the DNN accuracy for the testing set, since labeling each test input involves multiple persons (even with domain-specific knowledge) in a manual way and the testing set is large-scale. To relieve this problem, we propose a novel and practical approach, called PACE (which is short for P ractical AC curacy E stimation), which selects a small set of test inputs that can precisely estimate the accuracy of the whole testing set. In this way, the labeling costs can be largely reduced by just labeling this small set of selected test inputs. Besides achieving a precise accuracy estimation, to make PACE more practical it is also required that it is interpretable, deterministic, and as efficient as possible. Therefore, PACE first incorporates clustering to interpretably divide test inputs with different testing capabilities (i.e., testing different functionalities of a DNN model) into different groups. Then, PACE utilizes the MMD-critic algorithm, a state-of-the-art example-based explanation algorithm, to select prototypes (i.e., the most representative test inputs) from each group, according to the group sizes, which can reduce the impact of noise due to clustering. Meanwhile, PACE also borrows the idea of adaptive random testing to select test inputs from the minority space (i.e., the test inputs that are not clustered into any group) to achieve great diversity under the required number of test inputs. The two parallel selection processes (i.e., selection from both groups and the minority space) compose the final small set of selected test inputs. We conducted an extensive study to evaluate the performance of PACE based on a comprehensive benchmark (i.e., 24 pairs of DNN models and testing sets) by considering different types of models (i.e., classification and regression models, high-accuracy and low-accuracy models, and CNN and RNN models) and different types of test inputs (i.e., original, mutated, and automatically generated test inputs). The results demonstrate that PACE is able to precisely estimate the accuracy of the whole testing set with only 1.181%∼2.302% deviations, on average, significantly outperforming the state-of-the-art approaches.