graph neural networks

Existing Graph Neural Simulators (GNSs) suffer from two critical bottlenecks: (1) physical parameter fine-tuning necessitates full retraining, and (2) each new parameter configuration requires extensive, task-specific trajectory data collection, severely limiting cross-parameter generalization. To address this, we propose Meta-GNS—a meta-learning-based adaptive graph neural simulation framework that jointly integrates Conditional Neural Processes (CNPs) with neural operator architectures. By explicitly uncovering shared dynamical structures across multi-parameter regimes, Meta-GNS enables zero-shot adaptation to unseen material properties or physical parameters. Crucially, it encodes graph-structured trajectories without retraining and inherently suppresses long-horizon error accumulation. Empirically, on diverse dynamical prediction tasks—including fluid, elastic, and granular systems—Meta-GNS achieves simulation accuracy for unseen parameters that approaches that of an oracle model with full parameter knowledge, significantly outperforming state-of-the-art GNS methods.

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.

Graph neural networks (GNNs) suffer from high inference latency in relational database prediction, while hand-crafted features struggle to capture complex structural dependencies. Method: We propose LightRDL, a lightweight framework that synergistically integrates pretrained tabular models with GNNs for relational learning—decoupling responsibilities such that the GNN exclusively models structural dependencies among entities, while the tabular model efficiently encodes temporal and attribute features, eliminating the need for constructing and storing full historical graphs. Contribution/Results: LightRDL significantly reduces inference overhead while preserving expressive relational pattern modeling. On the RelBench benchmark, it achieves a 33% improvement in prediction accuracy over baseline GNNs and accelerates inference by 526×, thereby greatly enhancing feasibility for real-time prediction scenarios.

This paper addresses the limitation of standard Transformers in effectively modeling complex structural relationships. To this end, we propose Graph-Isomorphic Attention (GI-Attention), which reformulates self-attention as a graph isomorphism operation, explicitly incorporating the hierarchical relational reasoning capability of Graph Isomorphism Networks (GIN). Methodologically, we introduce the first sparse GIN-Attention fine-tuning paradigm: it disentangles an implicit sparse graph structure from the attention matrix and integrates the Principal Neighbourhood Aggregation (PNA) mechanism to enable master–neighborhood awareness. Compared to parameter-efficient methods such as LoRA, our approach substantially narrows the generalization gap. Empirical evaluation across bioinformatics, materials science, and language modeling tasks demonstrates improved dynamic adaptability to both local and global dependencies—achieving high transferability while maintaining low computational overhead.

Traditional neural networks struggle to explicitly model logical relationships such as part-whole hierarchies and lack symbolic reasoning capabilities. This work proposes a novel graph-structured neural architecture that encodes input data into a relational graph, where edges are drawn from a predefined set of primitive relations. The system employs a graph Hamiltonian operator to drive energy minimization, ensuring that the ground state satisfies all relational constraints. By embedding relational representations directly into fundamental components and integrating ultra-low-precision arithmetic with bit-level part-whole mechanisms, the approach achieves efficient symbolic reasoning and hierarchical structure construction while maintaining linear computational complexity. The model not only performs competitively on standard neural network tasks but also generates relation-aware positional encodings imbued with symbolic semantics, offering a new paradigm for vector-based representations.

Real-world graph data commonly suffer from poor scalability, dynamic evolution, directed heterophily, missing node features, and structural uncertainty—challenging the deployment of Graph Neural Networks (GNNs) in industrial applications such as social networks and recommender systems. To address these multifaceted challenges, we propose five complementary models: SIGN (for scalable static graphs), TGN (for temporal graphs), Dir-GNN (for directed heterophilous graphs), FP (for robust feature propagation under feature absence), and NuGget (for game-theoretic structural inference). Our framework systematically integrates temporal graph modeling, directed graph learning, robust feature propagation, and structure reasoning. It enables efficient training and strong generalization on graphs with millions of nodes. Extensive experiments demonstrate that each model achieves significant improvements over state-of-the-art methods on its respective task, effectively bridging the gap between academic GNN designs and industrial-scale graph requirements.

Existing graph neural networks (GNNs) struggle to capture the complex structural characteristics of neural architectures, while Transformers exhibit limited generalization on deep directed acyclic graphs (DAGs), primarily due to their neglect of topological relationships among sibling nodes—i.e., nodes sharing the same parent. To address this, we propose the Sibling-aware Token Mixer and the Bidirectional Graph Isomorphism Channel Mixer, which explicitly encode sibling relationships into DAG representations, thereby redefining the topological learning paradigm for neural architectures. Our method synergistically integrates GNNs’ structural awareness with Transformers’ long-range modeling capability, enhancing representational power without increasing parameter count. Experiments demonstrate that our approach significantly outperforms state-of-the-art methods on both accuracy and latency prediction tasks—achieving higher predictive fidelity and markedly improved cross-search-space transfer stability. This establishes a more robust foundation for neural architecture search.

This study addresses the fundamental challenge of deciphering the underlying structural and functional mechanisms—such as connectivity matrices, neuronal cell types, signaling dynamics, and latent external stimuli—from the complex spatiotemporal activity of heterogeneous neural systems. To this end, the authors propose an interpretable modeling framework based on graph neural networks that integrates neural dynamics simulation with graph structure learning. By doing so, the method overcomes the limitations of conventional black-box models while maintaining high predictive accuracy. Notably, it achieves the first joint inference of connectivity architecture, cell-type identity, signaling mechanisms, and hidden stimuli in large-scale simulated neural ensembles. The approach successfully reconstructs ground-truth connectivity matrices, neuronal types, and signal transmission functions at the scale of thousands of neurons and, in certain scenarios, accurately identifies unknown external inputs.

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.

This work elucidates the theoretical mechanisms underlying the superior performance of Graph Transformers over conventional Graph Convolutional Networks in node-level prediction tasks, particularly their ability to mitigate oversmoothing. By analyzing the Neural Network Gaussian Process (NNGP) limit under infinite width and infinite attention heads, the authors derive inter-layer kernels for nodes and edges that characterize how node features and graph structure propagate through the attention mechanism. For the first time from a Gaussian process perspective, they formally demonstrate that Graph Transformers structurally preserve community information and maintain discriminative deep node representations. The proposed kernel design, which integrates positional encodings with informative priors, is empirically validated on both synthetic and real-world graph datasets, yielding significant performance gains in deep architectures.