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.

Every graph hides a tree: through tree decomposition—a foundational tool in modern graph theory with broad applications such as in computational power networks, any network can be unfolded into a hierarchy of overlapping vertex bags whose backbone is a tree. Leveraging this powerful lens, we propose Topological Decomposition for Self-supervised Learning (TopDSL), a framework that injects multi-scale signals into graph representation learning. Concretely, we: 1) decompose the input graph into tree structures with bags representing local structural contexts; 2) compute bag-level roles via closeness centrality for nodes and local edge betweenness for edges, and aggregate these scores across bags to capture context-dependent importance (e.g., local structural bridges); 3) convert the resulting importance and attribute-stability scores into a context-aware augmentation policy that adaptively perturbs nodes, edges, and features—preserving local bridges, honoring multi-community vertices, and attenuating noisy global hubs; 4) construct a new structural similarity loss for contrastive learning, which fuses traditional graph-based proximity with a novel tree-based similarity derived from node co-occurrence in decomposition bags; 5) demonstrate that our framework achieves superior performance over state-of-the-art baselines on various graph learning benchmarks.

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.

Node equivalence is common in graphs, such as computing networks, encompassing automorphic equivalence (preserving adjacency under node permutations) and attribute equivalence (nodes with identical attributes). Despite their importance for learning node representations, these equivalences are largely ignored by existing graph models. To bridge this gap, we propose a GrAph self-supervised Learning framework with Equivalence (GALE) and analyze its connections to existing techniques. Specifically, we: 1) unify automorphic and attribute equivalence into a single equivalence class; 2) enforce the equivalence principle to make representations within the same class more similar while separating those across classes; 3) introduce approximate equivalence classes with linear time complexity to address the NP-hardness of exact automorphism detection and handle node-feature variation; 4) analyze existing graph encoders, noting limitations in message passing neural networks and graph transformers regarding equivalence constraints; 5) show that graph contrastive learning are a degenerate form of equivalence constraint; and 6) demonstrate that GALE achieves superior performance over baselines.

Graphs, fundamental in modeling various research subjects such as computing networks, consist of nodes linked by edges. However, they typically function as components within larger structures in real-world scenarios, such as in protein-protein interactions where each protein is a graph in a larger network. This study delves into the Graph-of-Net (GON), a structure that extends the concept of traditional graphs by representing each node as a graph itself. It provides a multi-level perspective on the relationships between objects, encapsulating both the detailed structure of individual nodes and the broader network of dependencies. To learn node representations within the GON, we propose a position-aware neural network for Graph-of-Net which processes both intra-graph and inter-graph connections and incorporates additional data like node labels. Our model employs dual encoders and graph constructors to build and refine a constraint network, where nodes are adaptively arranged based on their positions, as determined by the network’s constraint system. Our model demonstrates significant improvements over baselines in empirical evaluations on various datasets.

To be still yet still moving. - Do Hyun Choe

Graph self-supervised learning aims to learn the intrinsic graph representations from unlabeled data, with broad applicability in areas such as computing networks. Although graph contrastive learning (GCL) has achieved remarkable progress by generating perturbed views via data augmentation and optimizing sample similarity, it performs poorly in heterophilic graph scenarios (where connected nodes are likely to belong to different classes or exhibit dissimilar features). In heterophilic graphs, existing methods typically rely on random or carefully designed augmentation strategies (e.g., edge dropping) for contrastive views. However, such graph structures exhibit intricate edge relationships, where topological perturbations may completely alter the semantics of neighborhoods. Moreover, most methods focus solely on local contrastive signals while neglecting global structural constraints. To address these limitations, inspired by graph coloring, we propose a novel Coloring learning for heterophilic graph Representation framework, CoRep, which: 1) Pioneers a coloring classifier to generate coloring labels, explicitly minimizing the discrepancy between homophilic nodes while maximizing that of heterophilic nodes. A global positive sample set is constructed using multi-hop same-color nodes to capture global semantic consistency. 2) Introduces a learnable edge evaluator to guide the coloring learning dynamically and utilizes the edges' triplet relations to enhance its robustness. 3) Leverages Gumbel-Softmax to differentially discretize color distributions, suppressing noise via a redundancy constraint and enhancing intra-class compactness. Experimental results on 14 benchmark datasets demonstrate that CoRep significantly outperforms current state-of-the-art methods.

Limited-supervised multi-label learning (LML) leverages weak or noisy supervision for multi-label classification model training over data with label noise, which contain missing labels and/or redundant labels. Existing studies usually solve LML problems by assuming that label noise is independent of the input features and class labels, while ignoring the fact that noisy labels may depend on the input features (instance-dependent) and the classes (label-dependent) in many real-world applications. In this paper, we propose limited-supervised Multi-label Learning with Dependency Noise (MLDN) to simultaneously identify the instance-dependent and label-dependent label noise by factorizing the noise matrix as the outputs of a mapping from the feature and label representations. Meanwhile, we regularize the problem with the manifold constraint on noise matrix to preserve local relationships and uncover the manifold structure. Theoretically, we bound noise recover error for the resulting problem. We solve the problem by using a first-order scheme based on proximal operator, and the convergence rate of it is at least sub-linear. Extensive experiments conducted on various datasets demonstrate the superiority of our proposed method.

Multi-graph Multi-label learning (Mgml) aims to classify a set of objects of interest, such as text or images, using a bag-of-graphs representation. PreviousMgmlworks have limitations as they only learn labels at the bag level, lose structural information in learning by transferring graphs into instances, and cannot handle noisy labels. This paper presents a robustcoarseandfine-grainedNoise Multi-graph Multi-label (cfMGNML) learning framework that builds the learning model over the graphs and empowers label prediction at both thecoarse(bag) andfine-grained(graph in each bag) levels with noisy labels. To identify label noise, a label probability matrix is defined to act on the scoring function of each label, with a higher probability value indicating that the label is more likely to be the corresponding graph or bag label. The problem is regularized with the manifold constraint on the label probability matrix to preserve local relationships within the data and uncover its essential manifold structure. Meanwhile, a thresholding rank-loss objective is proposed to rank the labels for the graphs and bags and minimize the hamming loss at one step simultaneously. To tackle the non-convex optimization problem, an effective sub- gradient descent algorithm is developed. Experiments over various datasets demonstrate the proposed method achieves superior performance than the state-of-the-art algorithms.

Multi-instance learning (MIL) is a supervised learning where each example is a labeled bag with many instances. The typical MIL strategies are to train an instance-level feature extractor followed by aggregating instances features as bag-level representation with labeled information. However, learning such a bag-level representation highly depends on a large number of labeled datasets, which are difficult to get in real-world scenarios. In this paper, we make the first attempt to propose a robust Self-supervised Multi-Instance LEarning architecture with Structure awareness (SMILEs) that learns unsupervised bag representation. Our proposed approach is: 1) permutation invariant to the order of instances in bag; 2) structure-aware to encode the topological structures among the instances; and 3) robust against instances noise or permutation. Specifically, to yield robust MIL model without label information, we augment the multi-instance bag and train the representation encoder to maximize the correspondence between the representations of the same bag in its different augmented forms. Moreover, to capture topological structures from nearby instances in bags, our framework learns optimal graph structures for the bags and these graphs are optimized together with message passing layers and the ordered weighted averaging operator towards contrastive loss. Our main theorem characterizes the permutation invariance of the bag representation. Compared with state-of-the-art supervised MIL baselines, SMILEs achieves average improvement of 4.9%, 4.4% in classification accuracy on 5 benchmark datasets and 20 newsgroups datasets, respectively. In addition, we show that the model is robust to the input corruption.

Self-supervised learning on graph aims to learn graph representations in an unsupervised manner. While graph contrastive learning (GCL - relying on graph augmentation for creating perturbation views of anchor graphs and maximizing/minimizing similarity for positive/negative pairs) is a popular self-supervised method, it faces challenges in finding label-invariant augmented graphs and determining the exact extent of similarity between sample pairs to be achieved. In this work, we propose an alternative self-supervised solution that (i) goes beyond the label invariance assumption without distinguishing between positive/negative samples, (ii) can calibrate the encoder for preserving not only the structural information inside the graph, but the matching information between different graphs, (iii) learns isometric embeddings that preserve the distance between graphs, a by-product of our objective. Motivated by optimal transport theory, this scheme relays on an observation that the optimal transport plans between node representations at the output space, which measure the matching probability between two distributions, should be consistent to the plans between the corresponding graphs at the input space. The experimental findings include: (i) The plan alignment strategy significantly outperforms the counterpart using the transport distance; (ii) The proposed model shows superior performance using only node attributes as calibration signals, without relying on edge information; (iii) Our model maintains robust results even under high perturbation rates; (iv) Extensive experiments on various benchmarks validate the effectiveness of the proposed method.

Graphs are a powerful and versatile data structure that easily captures real life relationship. Multi-graph Multi-label learning (MGML) is a supervised learning task, which aims to learn a Multi-label classifier to label a set of objects of interest (e.g. image or text) with a bag-of-graphs representation. However, prior techniques on the MGML are developed based on transferring graphs into instances that does not fully utilize the structure information in the learning, and focus on learning the unseen labels only at the bag level. There is no existing work studying how to label the graphs within a bag that is of importance in many applications like image or text annotation. To bridge this gap, in this paper, we present a novel coarse and fine-grained Multi-graph Multi-label (cfMGML) learning framework which directly builds the learning model over the graphs and empowers the label prediction at both the coarse (aka. bag) level and fine-grained (aka. graph in each bag) level. In particular, given a set of labeled multi-graph bags, we design the scoring functions at both graph and bag levels to model the relevance between the label and data using specific graph kernels. Meanwhile, we propose a thresholding rank-loss objective function to rank the labels for the graphs and bags and minimize the hamming-loss simultaneously at one-step, which aims to address the error accumulation issue in traditional rank-loss algorithms. To tackle the non-convex optimization problem, we further develop an effective sub-gradient descent algorithm to handle high-dimensional space computation required in cfMGML. Experiments over various real-world datasets demonstrate cfMGML achieves superior performance than the state-of-arts algorithms.