graph-based hierarchy modeling

Existing heterogeneous graph neural networks (HGNNs) rely on predefined schemas and manual preprocessing for graphs lacking prior type information and exhibiting non-uniform feature formats, while large language model (LLM)-based approaches often neglect heterogeneity. Method: We propose LLM-GNN, a novel collaborative framework that enables end-to-end automatic format understanding, dynamic type induction, and cross-source feature alignment: an LLM performs semantic parsing of node/edge types to generate a structured schema; an adaptive module aligns heterogeneous features; and a lightweight GNN learns structured representations. Contribution/Results: Our method requires no type annotations or manual preprocessing. We provide theoretical guarantees on representation consistency and convergence. Evaluated on five standard heterogeneous graph benchmarks, LLM-GNN achieves an average 12.7% improvement in downstream task performance over state-of-the-art baselines.

To address the excessive memory and computational overhead in large-scale graph neural network (GNN) training, this paper proposes the first systematic framework integrating multi-scale graph representations. The method constructs hierarchical, multi-granularity graph structures via graph coarsening and introduces a coarse-to-fine training paradigm, subgraph-to-full-graph transfer strategy, and cross-scale gradient approximation mechanism—reducing computational complexity while preserving model accuracy. Experiments on multiple benchmark datasets demonstrate up to 40–65% memory reduction, 2.1–3.8× speedup in training time, and classification accuracy maintained or slightly improved. Crucially, this work is the first to deeply embed multi-scale graph representations across the entire GNN training pipeline, establishing a scalable and efficient paradigm for large-scale graph learning.

This paper addresses the challenge of modeling hierarchical graph lineages. Methodologically, it introduces an algebraic framework supporting exponential growth and multi-scale computation: (i) a stratified graph category is constructed; (ii) skeletonization operations and efficient unary operators—thickening and upgrading—are defined; (iii) bipartite graphs interconnect layers, while extension maps enable cross-scale distance metrics; and (iv) multi-level skeletonization and type construction mechanisms are developed. The key contributions are: (i) the first low-overhead, composable algebraic system for hierarchical graphs; and (ii) a unified foundation for adaptive mesh generation, function space construction, and scale-space modeling. The framework is successfully applied to approximating the continuous limit of deep neural networks and to multigrid numerical methods, significantly enhancing design flexibility and theoretical consistency in local sampling and optimization algorithms.

Existing graph tokenization methods exhibit limitations in hierarchical structure modeling and task adaptability: quantization strategies are often fixed or task-agnostic, leading to imbalanced structural representation and hindering dynamic multi-scale contribution adjustment without retraining the encoder. This paper proposes HQ-Graph, a Hierarchical Quantization Graph tokenization framework that enables dynamic multi-scale graph structural aggregation under a frozen encoder via a lightweight self-weighted gating mechanism, supporting task-adaptive discrete representation learning. Its core innovation lies in the organic integration of hierarchical quantization, discrete representation, learnable gating, and multi-scale aggregation. Experiments demonstrate that HQ-Graph consistently outperforms strong baselines on node classification and link prediction tasks, achieving superior performance at comparable computational cost—thereby balancing expressive power and parameter efficiency.

This work addresses the limitation of existing graph learning approaches, which typically operate in isolation within a single modality and task, thereby hindering the cross-task and cross-modal reuse of structural knowledge. To overcome this, the authors propose G-Substrate, a novel framework that models graph structures as persistent, shareable substrates. By unifying structural patterns and employing a role-interleaved training strategy, G-Substrate enables collaborative learning across multiple tasks and modalities. This approach facilitates the continuous accumulation and transfer of graph-structured knowledge, consistently outperforming both isolated training and conventional multi-task learning methods across diverse domains, modalities, and tasks.

This work addresses the limited generalization of existing node representation learning methods, which typically require dataset-specific training and hyperparameter tuning. The authors propose Node4All, the first framework enabling universal node representation learning across arbitrary graphs with a single model. Built upon a Channel Graph Transformer (CGT) architecture and powered by synthetic graph-driven self-supervised learning, Node4All eliminates the need for dataset-specific fine-tuning and supports both zero-shot and in-context learning. Evaluated on 25 benchmark datasets, it achieves an average rank of 5th, significantly outperforming most baselines and surpassing current graph foundation models under one-shot and in-context settings, thereby overcoming the dataset-specific limitations of conventional approaches.

This work addresses the problem of constructing low-dimensional geometric embeddings for directed acyclic graphs (DAGs) with ancestor–descendant relationships, aiming to avoid embedding dimensions that scale explosively with the number of nodes or graph depth. By leveraging structural properties—such as treewidth and the number of cross edges—and insights from geometric embedding theory, the authors propose a compact representation whose dimension depends only on these structural parameters rather than the total node count. Key contributions include a proof that any directed tree admits an exact reachability-preserving embedding in three dimensions, and an upper bound of \( O(t \log n) \) dimensions for DAGs of treewidth \( t \), accompanied by a nearly matching lower bound that reveals fundamental limits on dimensionality. Experiments on real-world datasets demonstrate that the method substantially reduces embedding dimension while maintaining high recall, outperforming existing approaches with theoretical guarantees.