Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Although a number of k-WL-based GNNs have been proposed to overcome this limitation, their computational cost increases rapidly with k, significantly restricting the practical applicability. Moreover, since the k-WL models mainly operate on node tuples, these k-WL-based GNNs cannot retain fine-grained node- or edge-level semantics required by attribution methods (e.g., Integrated Gradients), leading to the less interpretable problem. To overcome the above shortcomings, in this paper, we propose a novel Line Graph Aggregation Network (LGAN), that constructs a line graph from the induced subgraph centered at each node to perform the higher-order aggregation. We theoretically prove that the LGAN not only possesses the greater expressive power than the 2-WL under injective aggregation assumptions, but also has lower time complexity. Empirical evaluations on benchmarks demonstrate that the LGAN outperforms state-of-the-art k-WL-based GNNs, while offering better interpretability.

Graph neural networks (GNNs) have demonstrated impressive performance in a broad spectrum of fields, but always suffer from the generalization problem when confronted with out-of-distribution (OOD) scenarios. Information bottleneck (IB) principle, which endeavors to learn the minimally sufficient representations for downstream tasks, has been shown to be a promising strategy in dealing with this problem. However, the IB-based methods do not inherently distinguish between causal and non-causal parts in the graph, leading to underperforming OOD generalization ability. In this paper, we develop the Graph Causal Information Bottleneck (GCIB) framework, a causal extension of the IB for graph data, which is capable of jointly compressing abundant information and capturing causal dependency from the input graph. Specifically, we endow graph IB with the ability of maintaining causal control by incorporating the underlying causal structure and introducing intervention operation. On this basis, we formulate the learning objective for GCIB and present its specific implementation. Graph representations learned by GCIB can effectively preserve causal information that fundamentally determines graph properties, resulting in outstanding OOD generalization ability. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of GCIB over state-of-the-art baselines.

In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters, resulting in a family of separated subgraphs. We individually employ the local graph convolution units as the local structure to further compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. Since these subgraphs are separated by different clusters and the structural information cannot be propagated between them, the local convolution operation can significantly avoid the over-smoothing problem caused by message passing through edges in most existing Graph Neural Networks (GNNs). By hierarchically performing the proposed procedures on the resulting coarsened graph, the proposed SSHPool can effectively extract the hierarchical global features of the original graph structure, encapsulating rich intrinsic structural characteristics. Furthermore, we develop an end-to-end GNN framework associated with the SSHPool module for graph classification. Experimental results demonstrate the superior performance of the proposed model on real-world datasets.

Graph Neural Networks (GNNs) perform well on in-distribution data but often fail under out-of-distribution (OOD) shifts due to reliance on spurious patterns. To address this, we propose CauVQ, a causal vector quantization framework that improves OOD generalization by identifying and leveraging invariant substructures that are causally predictive. To construct stable and symbolic graph representations, CauVQ decomposes each input into local substructures and maps them to a discrete codebook of prototypical motifs. This enables consistent and interpretable encoding across diverse graph domains. To isolate the causal substructures, we maximize their mutual information with graph labels and refine their representations using a learnable interaction matrix and a causal attention mechanism. Furthermore, we introduce a counterfactual regularization strategy to enforce prediction stability under substructure perturbations, encouraging the model to focus on truly causal patterns rather than superficial shortcuts. Extensive experiments across standard and OOD benchmarks demonstrate that CauVQ consistently outperforms state-of-the-art baselines in robustness and interpretability. Our framework offers a promising step toward reliable, explainable, and distribution-aware graph learning.

Graph-based representations are powerful tools for analyzing structured data. In this paper, we propose a novel model to learn Deep Hierarchical Attention-based Kernelized Representations (DHAKR) for graph classification. To this end, we commence by learning an assignment matrix to hierarchically map the substructure invariants into a set of composite invariants, resulting in hierarchical kernelized representations for graphs. Moreover, we introduce the feature-channel attention mechanism to capture the interdependencies between different substructure invariants that will be converged into the composite invariants, addressing the shortcoming of discarding the importance of different substructures arising in most existing R-convolution graph kernels. We show that the proposed DHAKR model can adaptively compute the kernel-based similarity between graphs, identifying the common structural patterns over all graphs. Experiments demonstrate the effectiveness of the proposed DHAKR model.

In this paper, we propose a new model to learn Adaptive Kernel-based Representations (AKBR) for graph classification. Unlike state-of-the-art R-convolution graph kernels that are defined by merely counting any pair of isomorphic substructures between graphs and cannot provide an end-to-end learning mechanism for the classifier, the proposed AKBR approach aims to define an end-to-end representation learning model to construct an adaptive kernel matrix for graphs. To this end, we commence by leveraging a novel feature-channel attention mechanism to capture the interdependencies between different substructure invariants of original graphs. The proposed AKBR model can thus effectively identify the structural importance of different substructures, and compute the R-convolution kernel between pairwise graphs associated with the more significant substructures specified by their structural attentions. Furthermore, the proposed AKBR model employs all sample graphs as the prototype graphs, naturally providing an end-to-end learning architecture between the kernel computation as well as the classifier. Experimental results show that the proposed AKBR model outperforms existing state-of-the-art graph kernels and deep learning methods on standard graph benchmarks.

The over-smoothing has emerged as a major challenge in the development of Graph Neural Networks (GNNs). While existing state-of-the-art methods effectively mitigate the diminishing distance between nodes and improve the performance of node classification, they tend to be elusive for graph-level tasks. This paper introduces a novel entropy-based perspective to explore the over-smoothing problem, simultaneously enhancing the distinguishability of non-isomorphic graphs. We provide a theoretical analysis of the relationship between the smoothness and the entropy for graphs, highlighting how the over-smoothing in high-entropic regions negatively impact the graph classification performance. To tackle this issue, we propose a simple yet effective method to Sample and Discretize node features in high-Entropic regions (SDE), aiming to preserve the critical and complicated structural information. Moreover, we introduce a new evaluation metric to assess the over-smoothing for graph-level tasks, focusing on node distributions. Experimental results demonstrate that the proposed SDE method significantly outperforms existing state-of-the-art methods, establishing a new benchmark in the field of GNNs.

In this paper, we propose a Hierarchical Aligned Subtree Convolutional Network (HA-SCN) for graph classification. Our idea is to transform graphs of arbitrary sizes into fixed-sized aligned graphs and construct a normalized K-layer m-ary subtree for each node in the aligned graphs. By sliding convolutional filters over the entire subtree at each node, we define a novel subtree convolution and pooling operation that hierarchically abstracts node-level information. We demonstrate that the proposed HA-SCN model not only realizes the convolution mechanism similar to the Convolutional Neural Networks (CNNs), which have the characteristics of weight sharing and fixed-sized receptive fields, but also effectively mitigates the over-squashing problem. Meanwhile, it establishes the correspondence information between nodes, alleviating the information loss issue. Experimental results on various benchmark graph datasets show that our approach achieves state-of-the-art performance in graph classification tasks.

In this paper, we propose a family of novel Deep Hierarchical Transitive-Aligned Graph Kernels (DHTAGK) for graph classification. To this end, we commence by developing a new Hierarchical Aligned Graph Auto-Encoder (HA-GAE) to construct transitive-aligned embedding graphs that encapsulate the structural correspondence information between graphs. The DHTAGK kernels then measure either the Jensen-Shannon Divergence between the adjacency matrices or the Gaussian kernel between the node feature matrices of the embedding graphs. Unlike the classical R-convolution kernels and node-based alignment kernels, the DHTAGK kernels can capture the transitive structural correspondence information and thus ensure the positive definiteness. Furthermore, the HA-GAE enables the DHTAGK kernels to simultaneously reflect both local and global graph structures and identify common structural patterns. Experimental results show that the DHTAGK kernels outperform state-of-the-art graph kernels and deep learning methods on benchmark datasets.

Graph Neural Networks (GNNs) are powerful tools for graph learning, but one of the important challenges is how to effectively extract representations for graph-level tasks. In this paper, we propose an end-to-end Simple Clustering Hierarchical Pooling (SCHPool) operation, which is based on Top-K node selection for learning expressive graph representations. Specifically, SCHPool considers each node and its local neighborhood as a cluster, and introduces a novel multi-view scoring function to evaluate node importance. Based on these scores, clusters centered around the Top-K nodes are retained. This design eliminates the need for complex clustering operations, significantly reducing computational overhead. Furthermore, during the coarsening process, SCHPool employs a lightweight yet comprehensive attention mechanism to adaptively aggregate both the node features within clusters and the edge connectivity strengths between clusters. This facilitates the construction of more informative coarsened graphs, enhancing model performance. Experimental results demonstrate the effectiveness of the proposed model.

In recent years, the out-of-distribution (OOD) generalization problem of graph data has received widespread attention, which refers to how a model maintains strong generalization performance when there are distribution shifts between training and testing data. Invariant learning is considered as an effective solution for solving the OOD generalization problem. However, graph data has more complex structures than Euclidean data and contains a variety of distribution shifts. Therefore, the captured invariant features may include spurious invariant components, which can drop the generalization performance of the model. To solve this problem, we propose a new invariant learning model named causal information bottleneck learning model (CIBL). Specifically, we introduce information bottleneck principle to eliminate the impact of spurious invariant components on the model by compressing the learned redundant information. In this way, the model can learn causal invariant features, which can ensure the generalization performance of the model. We conduct several experiments in different OOD scenarios, and the results demonstrate that the CIBL model outperforms other baseline models.

Graph contrastive learning (GraphCL) is widely used in recommendation systems. However, GraphCL recommendation systems are still plagued by the popularity bias problem. Besides, during the contrastive task, data augmentation may damage the original data structure information. To solve these problems, we propose a new GraphCL recommendation model, namely GCR-DDA, which contains three key modules: collaborative relation encoder (CRE), debiasing channel and structure preserving channel. The CRE is used to integrate local neighborhood information. In the debiasing channel, noise-based embedding augmentation is designed to mitigate the popularity bias problem of the skewed distribution. In the structure preserving channel, the variational graph auto-encoder (VGAE) is implied as a graph generation model for data augmentation. Contrastive task is constructed from the two channels, and is integrated with the recommendation task in a joint optimization model. Results of extensive experiments on three datasets show that GCR-DDA outperforms baselines.

The problem of over-smoothing has emerged as a fundamental issue for Graph Convolutional Networks (GCNs). While existing efforts primarily focus on enhancing the discriminability of node representations for node classification, they tend to overlook the over-smoothing at the graph level, significantly influencing the performance of graph classification. In this paper, we provide an explanation of the graph-level over-smoothing phenomenon and propose a novel Adaptive Multi-Viewed Subgraph Convolutional Network (MultiNet) to address this challenge. Specifically, the MultiNet introduces a local subgraph convolution module that adaptively divides each input graph into multiple subgraph views. Then a number of subgraph-based view-specific convolution operations are applied to constrain the extent of node information propagation over the original global graph structure, not only mitigating the over-smoothing issue but also generating more discriminative local node representations. Moreover, we develop an alignment-based readout that establishes correspondences between nodes over different graphs, thereby effectively preserving the local node-level structure information and improving the discriminative ability of the resulting graph-level representations. Theoretical analysis and empirical studies show that the MultiNet mitigates the graph-level over-smoothing and achieves excellent performance for graph classification.

Cluster ensemble is a very important tool that aggregates several base clusterings to generate a single output clustering with improved robustness and stability. However, the quality of the final clustering is often affected by uncertainties on the generation and integration of base clusterings. In this paper, we develop an information-theoretical framework which makes an effort to obtain a final clustering with high consensus on both the original data set and the base clustering set by minimizing the two uncertainties of cluster ensemble. In this framework, we provide a weighted consensus measure based on information entropy to evaluate the quality of a clustering, the similarity between clusters and the similarity between objects. Based on the measure, we propose three weighted cluster ensemble algorithms with different ensemble strategies in the framework, including the weighted feature consensus algorithm, the weighted relabeling consensus algorithm and the weighted pairwise-similarity consensus algorithm. In the experimental analysis, we compare the proposed algorithms with other existing clustering ensemble algorithms on several data sets. The comparison results illustrate the proposed algorithms are very effective and robust.