GJDNet: Robust Graph Neural Networks via Joint Disentangled Learning Against Adversarial Attacks

Graph Neural Networks (GNNs) are vulnerable to adversarial attacks, which inherently invert connectivity patterns by introducing disassortative edges in assortative graphs and assortative edges in disassortative graphs. This structural inversion creates structure-feature mismatches that disrupt neighborhood aggregation across different graph types. However, we find that existing defenses are limited, as they either treat neighborhoods as monolithic under fixed assortativity assumptions or rely on standard softmax classifiers that fail to account for perturbation-induced representation shifts. To further exploit this observation, we adopt a robustness perspective that jointly disentangles node representations and decision spaces, isolating perturbation effects while enforcing well-separated decision regions. Based on this principle, we propose Graph Joint Disentanglement Network (GJDNet), a unified framework for robust node classification across diverse graph assortativity regimes. GJDNet enhances robustness at both representation and decision levels: it employs feature-driven soft structural disentanglement with skewness-aware neighbor filtering to suppress perturbation-induced structure-feature mismatches, and introduces a Spherical Decision Boundary (SDB) to promote intra-class compactness and inter-class separation in the embedding space, thereby stabilizing decision boundaries under perturbations. Theoretical analysis provides insights into the effectiveness of the proposed disentangled representation and decision mechanisms, while extensive experiments demonstrate that GJDNet consistently achieves strong robustness across graphs with different connectivity regimes.

Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks

Graphs effectively characterize relational data, driving graph representation learning methods that uncover underlying predictive information. As state-of-the-art approaches, Graph Neural Networks (GNNs) enable end-to-end learning for diverse tasks. Recent disentangled graph representation learning enhances interpretability by decoupling independent factors in graph data. However, existing methods often implicitly and coarsely characterize graph structures, limiting structural pattern analysis within the graph. This paper proposes the Graph Optimal Matching Kernel Convolutional Network (GOMKCN) to address this limitation. We view graphs as node-centric subgraphs, where each subgraph acts as a structural factor encoding position-specific information. This transforms graph prediction into structural pattern recognition. Inspired by CNNs, GOMKCN introduces the Graph Optimal Matching Kernel (GOMK) as a convolutional operator, computing similarities between subgraphs and learnable graph filters. Mathematically, GOMK maps subgraphs and filters into a Hilbert space, representing graphs as point sets. Disentangled representations emerge from projecting subgraphs onto task-optimized filters, which adaptively capture relevant structural patterns via gradient descent. Crucially, GOMK incorporates local correspondences in similarity measurement, resolving the trade-off between differentiability and accuracy in graph kernels. Experiments validate that GOMKCN achieves superior accuracy and interpretability in graph pattern mining and prediction. The framework advances the theoretical foundation for disentangled graph representation learning.