Multi-graph multi-label learning (MGML) represents each object as a bag-of-graphs with multiple labels, but demands large-scale labeled data whose acquisition is often difficult and costly. Self-supervised contrastive learning (SCL) mitigates label dependence by leveraging data augmentation to construct discriminative pretext tasks, proving effective for multi-instance learning. However, when applied to MGML, SCL faces two key challenges: (1) it distinguishes individual instances by their differences, whereas MGML requires modeling label correlations; (2) it assumes semantic invariance under augmentation, but structural perturbations in MGML alter label semantics. To tackle these challenges, we propose a self-suPervised contrastive rE-learning framework for mulTi-grAph multi-labeL classification (PETAL). Specifically, to model label correlations, we first define a unified label space to learn label prototypes and align features with them, yielding prototype-aligned representations. We then design a multi-granularity contrastive loss over these representations, which captures label dependencies by contrasting at the bag level, graph level, and bag-graph level. Moreover, to ensure semantic invariance, we develop a contrastive re-learning strategy based on prototype-aligned representations to generate augmentation-free positive samples. This guarantees consistent multi-label distributions without structural perturbations. Experiments on six datasets demonstrate that PETAL achieves an average improvement of 4.12% over state-of-the-art self-supervised and supervised baselines.

Multi-Graph Learning (MGL) is a fundamental machine learning paradigm that represents objects as bags-of-graphs, each encoding a distinct structural property, and has broad applications in bioinformatics, chemistry, computing power networks, and software defect detection. However, the inherent scarcity of labeled data poses a significant bottleneck for supervised MGL approaches. While self-supervised contrastive learning offers a compelling solution, its direct application to MGL faces three key challenges: (1) existing graph neural networks, primarily for single-graph modeling, struggle to yield discriminative bag-level representations from bags-of-graphs; (2) conventional contrastive objectives are limited to single-level settings, failing to capture cross-hierarchical dependencies; and (3) standard data augmentation often disrupts intrinsic graph and bag structures, undermining semantic consistency. To address these issues, we propose the Hierarchical Graph-Bag-Network (HGBN), a self-supervised MGL framework that constructs hierarchical representations in the form of a graph-bag-network. HGBN employs an asymmetric hierarchical graph neural network to learn discriminative graph-level and bag-level representations, introduces cross-hierarchical contrastive objectives to align graph-level and bag-level semantics, and leverages the asymmetric network outputs to form positive and negative pairs, preserving intrinsic structural and semantic consistency. Experiments on eight benchmark multi-graph datasets demonstrate that HGBN consistently outperforms both supervised and self-supervised state-of-the-art baselines, achieving average improvements of 4.82% in accuracy and F1 score.

Abstract Software quality is key to the success of software systems. Modern software systems are growing in their worth based on industry needs and becoming more complex, which inevitably increases the possibility of more defects in software systems. Software repairing is time‐consuming, especially locating the source files related to specific software defect reports. To locate defective source files more quickly and accurately, automated software defect location technology is generated and has a huge application value. The existing deep learning‐based software defect location method focuses on extracting the semantic correlation between the source file and the corresponding defect reports. However, the extensive code structure information contained in the source files is ignored. To this end, we propose a software defect location method, namely, multi‐graph learning‐based software defect location (MGSDL). By extracting the program dependency graphs for functions, each source file is converted into a graph bag containing multiple graphs (i.e., multi‐graph). Further, a multi‐graph learning method is proposed, which learns code structure information from multi‐graph to establish the semantic association between source files and software defect reports. Experiments' results on four publicly available datasets, AspectJ, Tomcat, Eclipse UI, and SWT, show that MGSDL improves on average 3.88%, 5.66%, 13.23%, 9.47%, and 3.26% over the competitive methods in five evaluation metrics, rank@10, rank@5, MRR, MAP, and AUC, respectively.