adaptive graph convolutions

Standard convolutional operations cannot be directly applied to graph-structured data due to its irregular, non-Euclidean topology. Method: This paper proposes Graph Kernel-driven Learnable Structural Convolution (GK-Conv), a purely structural, end-to-end modeling framework operating directly on non-Euclidean graph domains. GK-Conv eliminates explicit graph embedding and instead constructs a parameterized, structural convolutional operator grounded in generic graph kernel functions—enabling plug-and-play integration of arbitrary graph kernels and generating CNN-style, interpretable structural masks. The model is fully differentiable and optimized via ablation-guided hyperparameter analysis. Contribution/Results: GK-Conv achieves state-of-the-art performance across multiple graph classification and regression benchmarks, empirically validating the central claim that strong generalization can be attained using topology alone—without node or edge features.

Traditional message-passing neural networks (MPNNs) suffer from oversmoothing with increasing depth and struggle to jointly capture global and local graph structures. To address this, we propose a Laplacian eigenvector learning-based pretraining framework for graph neural networks: it employs a self-supervised task that predicts low-frequency eigenvectors of the graph Laplacian matrix, enabling implicit modeling of spectral structural properties in an unsupervised manner. Our method is inherently structure-aware, domain-agnostic, and supports inductive generalization; moreover, it accommodates synthetic node features when real features are sparse. Extensive experiments demonstrate that models pretrained with our framework significantly outperform baselines across diverse downstream graph tasks—including node classification, link prediction, and graph classification—exhibiting superior structural understanding and cross-domain generalization capability.

Existing GNN methods (e.g., GAMLP, ImprovingTE) rely on predefined sampling strategies for k-hop structural learning, resulting in poor generalizability and weak robustness. To address this, we propose DRTR (Distance Recomputator & Topology Reconstructor), an adaptive neighborhood reconstruction framework that— for the first time—jointly models distance recalibration and dynamic local topology reconstruction. DRTR employs graph-property-driven distance re-evaluation, coreset-inspired neighborhood selection, and multi-hop-structure-aware message passing to achieve context-aware and robust k-hop information aggregation. Evaluated on multiple benchmark datasets, DRTR consistently outperforms state-of-the-art models in both predictive accuracy and stability under noisy or mislabeled conditions.

Existing studies lack quantitative theoretical analysis of the differences in optimization and generalization performance between graph neural networks (GNNs) and multilayer perceptrons (MLPs). Method: Leveraging feature learning theory, this paper provides the first rigorous analysis of two-layer graph convolutional networks (GCNs) trained via gradient descent, modeling ReLU^q activation functions and spectral properties of the expected degree matrix D, under a structure-guided signal-noise separation framework. Contribution/Results: We theoretically prove that graph convolution explicitly exploits graph structure to significantly enhance signal learning while suppressing noise memorization, thereby expanding the benign overfitting regime by approximately √D^{q−2} compared to CNNs. This constitutes the first quantitative characterization of the fundamental generalization advantage of GNNs over MLPs. Extensive simulations corroborate the superior generalization and robustness of GCNs predicted by our theory.

To address the distortion of graph properties and insufficient structural diversity caused by conventional data augmentation in graph classification, this work investigates graph spectral characteristics and, for the first time, identifies the critical role of low-frequency spectral components in conserving global graph properties—such as connectivity and clustering coefficient. We propose Dual-Prism (DP-Noise/DP-Mask), a spectral-aware augmentation framework grounded in graph Laplacian spectral decomposition. It imposes explicit constraints in the low-frequency subspace and synergistically integrates differentiable noise injection with masked reconstruction to jointly optimize property preservation and structural diversification. Evaluated on multiple standard graph classification benchmarks, our method improves GNN generalization performance by 2.3–5.1% on average and reduces bias in key topological properties by over 67%. The framework is both interpretable—owing to its spectral foundation—and practically deployable.

Existing deep learning models struggle to effectively encode spatial, topological, and semantic structural information inherent in images. This work systematically evaluates the impact of various visual graph construction strategies on image classification performance within a unified three-layer Graph Convolutional Network (GCN) framework. For the first time, it demonstrates that the graph structure itself plays a decisive role in model performance. The study underscores the critical importance of the graph construction preprocessing stage, providing empirical evidence that well-designed graph structures substantially enhance classification accuracy. These findings offer both methodological guidance and practical justification for graph structure selection and preprocessing in visual graph neural networks.