graph-based region modeling

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.

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.

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.

This work addresses the limited representational capacity of Graph Neural Networks (GNNs) when node features reside in uncountable spaces—e.g., continuous or infinite-dimensional domains. To overcome restrictive assumptions of countable features and strict injectivity, we propose Soft Isomorphism-aware Relational Graph Convolutional Networks (SIR-GCN). SIR-GCN replaces conventional discrete feature handling with pseudo-metric space modeling and soft injective functions, enabling context-aware, anisotropic, and dynamic message passing. We theoretically establish that SIR-GCN is a strict generalization of classical GNNs. Empirically, SIR-GCN achieves state-of-the-art performance on both node classification and graph-level property prediction tasks across synthetic benchmarks and standard datasets—including Cora, PPI, and ZINC—demonstrating substantially improved modeling capability and generalization for uncountable feature spaces.

Deepening graph neural networks (GNNs) is hindered by oversmoothing and over-squashing—where the latter arises from inherent topological constraints on long-range information propagation and is often confounded with training dynamics (e.g., gradient vanishing), complicating rigorous evaluation of graph rewiring methods. This paper introduces the first training-free message-passing evaluation framework, explicitly decoupling over-squashing effects from optimization artifacts to isolate the intrinsic impact of topological rewiring. We systematically assess diverse rewiring strategies—including *k*-hop expansion and random edge addition—on node- and graph-level classification tasks. Leveraging parameter-free message passing and multi-scale graph structural analysis across multiple real-world datasets, our experiments reveal that most rewiring techniques yield no statistically significant performance gain. These findings challenge the widely held assumption of universal efficacy for rewiring and expose fundamental limitations in current rewiring paradigms.

Existing graph representations—such as adjacency matrices—are incompatible with the text-processing paradigm of large language models (LLMs). To address this, we propose a reversible, locally structure-preserving mapping from graphs to instruction sequences: graphs are encoded into compact, deterministic instruction strings via adjacency matrix decomposition, yielding a parseable textual representation; a custom reversible parser enables lossless reconstruction. This work establishes the first bridge between graph algebra and LLM-native textual processing, simultaneously ensuring structural fidelity and sequence conciseness. Experiments demonstrate that our representation significantly improves LLM performance on graph modeling tasks—including graph classification and link prediction—validating both its effectiveness and generalizability across diverse graph domains.

This work addresses the limited transparency of graph neural network (GNN) inference by proposing a novel graph convolution approach that performs message passing within a node-level concept space, thereby enabling the first purely concept-space-based graph convolution. The method integrates raw input features with learnable concept representations and introduces a hybrid edge-weighting mechanism that combines structural priors with attention to enhance interpretability of concept evolution throughout the message-passing process. Experimental results demonstrate that the proposed approach achieves competitive task accuracy while significantly improving the understanding of GNNs’ internal decision-making logic.

This study systematically investigates the effectiveness boundaries and practical value of Graph Neural Networks (GNNs) across twelve application domains. Building upon a unified design space, it derives both spectral and spatial formulations of GNNs from first principles, analyzes their expressive power through the lens of the Weisfeiler–Leman test, and evaluates domain-specific graph construction strategies and architectural choices. The work establishes the first cross-domain analytical framework that disentangles genuine performance gains from baseline biases, uncovering common challenges such as heterophily, scaling effects, and deployment gaps. It clarifies the applicability limits of GNNs, highlights the discrepancy between leaderboard-topping models and deployable ones, and offers constraint-aware practical guidelines to address issues including oversmoothing, over-squashing, and distributional shifts.

To address the oversmoothing problem in unsupervised node representation learning on heterophilic graphs—where excessive neighborhood aggregation causes embedding collapse and intra-class confusion—this paper proposes an adaptive graph convolutional regulation framework. First, it dynamically modulates message-passing strength in an unsupervised setting, mitigating homogenization induced by neighborhood aggregation. Second, it introduces a feature-driven implicit clustering mechanism that discovers high-quality pseudo-classes without ground-truth labels. Third, it jointly optimizes intra-class compactness and inter-class separability by integrating contrastive learning with adaptive message passing. Extensive experiments across 14 benchmark datasets demonstrate significant improvements over 15 state-of-the-art baselines; notably, the method achieves new state-of-the-art performance on low-homophily graphs, with consistent gains in both node classification and clustering metrics.

Vision GNN inference suffers from high computational overhead and serial bottlenecks due to dynamic graph construction at each layer. This work proposes a first-order lookahead graph construction mechanism that decouples graph building from feature updating: the graph for the current layer is constructed using features from the previous layer, while the graph for the next layer is pre-constructed using current-layer features, enabling parallel execution of graph construction and message passing. A streaming FPGA-based architecture is designed, integrating kNN graph construction and feature update engines with node- and channel-level parallelism, eliminating explicit edge storage. Implemented on an Alveo U280, the approach achieves up to 95.7× speedup over CPU and 8.5× over GPU, delivering the first end-to-end pipelined acceleration for Vision GNNs while preserving model accuracy and enabling real-time inference.