Two Sides of the Same Optimization Coin: Model Degradation and Representation Collapse in Graph Foundation Models

Graph foundation models, inspired by the success of LLMs, are designed to learn the optimal embedding from multi-domain TAGs for the downstream cross-task generalization capability. During our investigation, graph VQ-MAE stands out among the increasingly diverse landscape of GFM architectures. This is attributed to its ability to jointly encode topology and textual attributes from multiple domains into discrete embedding spaces with clear semantic boundaries. Despite its potential, domain generalization conflicts cause imperceptible pitfalls. In this paper, we instantiate two of them, and they are just like two sides of the same GFM optimization coin - Side 1 Model Degradation: The encoder and codebook fail to capture the diversity of inputs; Side 2 Representation Collapse: The hidden embedding and codebook vector fail to preserve semantic separability due to constraints from narrow representation subspaces. These two pitfalls (sides) collectively impair the decoder and generate the low-quality reconstructed supervision, causing the GFM optimization dilemma during pre-training (coin). Through empirical investigation, we attribute the above challenges to Information Bottleneck and Regularization Deficit. To address them, we propose MoT (Mixture-of-Tinkers) - (1) Information Tinker for Two Pitfalls, which utilizes an edge-wise semantic fusion strategy and a mixture-of-codebooks with domain-aware routing to improve information capacity. (2) Regularization Tinker for Optimization Coin, which utilizes two additional regularizations to further improve gradient supervision in our proposed Information Tinker. Notably, as a flexible architecture, MoT adheres to the scaling laws of GFM, offering a controllable model scale. Compared to SOTA baselines, experiments on 22 datasets across 6 domains demonstrate that MoT achieves significant improvements in supervised, few-shot, and zero-shot scenarios.

Efficient Exact Resistance Distance Computation on Small-Treewidth Graphs: a Labelling Approach

Resistance distance computation is a fundamental problem in graph analysis, yet existing random walk-based methods are limited to approximate solutions and suffer from poor efficiency on small-treewidth graphs (e.g., road networks). In contrast, shortest-path distance computation achieves remarkable efficiency on such graphs by leveraging cut properties and tree decompositions. Motivated by this disparity, we first analyze the cut property of resistance distance. While a direct generalization proves impractical due to costly matrix operations, we overcome this limitation by integrating tree decompositions, revealing that the resistance distance $r(s,t)$ depends only on labels along the paths from $s$ and $t$ to the root of the decomposition. This insight enables compact labelling structures. Based on this, we propose \treeindex, a novel index method that constructs a resistance distance labelling of size $O(n \cdot h_{\mathcal{G}})$ in $O(n \cdot h_{\mathcal{G}}^2 \cdot d_{\max})$ time, where $h_{\mathcal{G}}$ (tree height) and $d_{\max}$ (maximum degree) behave as small constants in many real-world small-treewidth graphs (e.g., road networks). Our labelling supports exact single-pair queries in $O(h_{\mathcal{G}})$ time and single-source queries in $O(n \cdot h_{\mathcal{G}})$ time. Extensive experiments show that TreeIndex substantially outperforms state-of-the-art approaches. For instance, on the full USA road network, it constructs a $405$ GB labelling in $7$ hours (single-threaded) and answers exact single-pair queries in $10^{-3}$ seconds and single-source queries in $190$ seconds--the first exact method scalable to such large graphs.

A Comprehensive Data-centric Overview of Federated Graph Learning

In the era of big data applications, Federated Graph Learning (FGL) has emerged as a prominent solution that reconcile the tradeoff between optimizing the collective intelligence between decentralized datasets holders and preserving sensitive information to maximum. Existing FGL surveys have contributed meaningfully but largely focus on integrating Federated Learning (FL) and Graph Machine Learning (GML), resulting in early stage taxonomies that emphasis on methodology and simulated scenarios. Notably, a data centric perspective, which systematically examines FGL methods through the lens of data properties and usage, remains unadapted to reorganize FGL research, yet it is critical to assess how FGL studies manage to tackle data centric constraints to enhance model performances. This survey propose a two-level data centric taxonomy: Data Characteristics, which categorizes studies based on the structural and distributional properties of datasets used in FGL, and Data Utilization, which analyzes the training procedures and techniques employed to overcome key data centric challenges. Each taxonomy level is defined by three orthogonal criteria, each representing a distinct data centric configuration. Beyond taxonomy, this survey examines FGL integration with Pretrained Large Models, showcases realistic applications, and highlights future direction aligned with emerging trends in GML.

When LLMs meet open-world graph learning: a new perspective for unlabeled data uncertainty

Recently, large language models (LLMs) have significantly advanced text-attributed graph (TAG) learning. However, existing methods inadequately handle data uncertainty in open-world scenarios, especially concerning limited labeling and unknown-class nodes. Prior solutions typically rely on isolated semantic or structural approaches for unknown-class rejection, lacking effective annotation pipelines. To address these limitations, we propose Open-world Graph Assistant (OGA), an LLM-based framework that combines adaptive label traceability, which integrates semantics and topology for unknown-class rejection, and a graph label annotator to enable model updates using newly annotated nodes. Comprehensive experiments demonstrate OGA's effectiveness and practicality.

Toward Data-centric Directed Graph Learning: An Entropy-driven Approach

The directed graph (digraph), as a generalization of undirected graphs, exhibits superior representation capability in modeling complex topology systems and has garnered considerable attention in recent years. Despite the notable efforts made by existing DiGraph Neural Networks (DiGNNs) to leverage directed edges, they still fail to comprehensively delve into the abundant data knowledge concealed in the digraphs. This data-level limitation results in model-level sub-optimal predictive performance and underscores the necessity of further exploring the potential correlations between the directed edges (topology) and node profiles (feature and labels) from a data-centric perspective, thereby empowering model-centric neural networks with stronger encoding capabilities. In this paper, we propose \textbf{E}ntropy-driven \textbf{D}igraph knowl\textbf{E}dge distillatio\textbf{N} (EDEN), which can serve as a data-centric digraph learning paradigm or a model-agnostic hot-and-plug data-centric Knowledge Distillation (KD) module. The core idea is to achieve data-centric ML, guided by our proposed hierarchical encoding theory for structured data. Specifically, EDEN first utilizes directed structural measurements from a topology perspective to construct a coarse-grained Hierarchical Knowledge Tree (HKT). Subsequently, EDEN quantifies the mutual information of node profiles to refine knowledge flow in the HKT, enabling data-centric KD supervision within model training. As a general framework, EDEN can also naturally extend to undirected scenarios and demonstrate satisfactory performance. In our experiments, EDEN has been widely evaluated on 14 (di)graph datasets (homophily and heterophily) and across 4 downstream tasks. The results demonstrate that EDEN attains SOTA performance and exhibits strong improvement for prevalent (Di)GNNs.

FedC4: Graph Condensation Meets Client-Client Collaboration for Efficient and Private Federated Graph Learning

Federated Graph Learning (FGL) is an emerging distributed learning paradigm that enables collaborative model training over decentralized graph-structured data while preserving local privacy. Existing FGL methods can be categorized into two optimization architectures: (1) the Server-Client (S-C) paradigm, where clients upload local models for server-side aggregation; and (2) the Client-Client (C-C) paradigm, which allows direct information exchange among clients to support personalized training. Compared to S-C, the C-C architecture better captures global graph knowledge and enables fine-grained optimization through customized peer-to-peer communication. However, current C-C methods often broadcast identical and redundant node embeddings, incurring high communication costs and privacy risks. To address this, we propose FedC4, a novel framework that combines graph Condensation with Client-Client Collaboration. Instead of transmitting raw node-level features, FedC4 distills each client's private graph into a compact set of synthetic node embeddings, reducing communication overhead and enhancing privacy. In addition, FedC4 introduces three modules that allow source clients to send distinct node representations tailored to target clients'graph structures, enabling personalized optimization with global guidance. Extensive experiments on eight real-world datasets show that FedC4 outperforms state-of-the-art baselines in both performance and communication efficiency.

Towards Unbiased Federated Graph Learning: Label and Topology Perspectives

Federated Graph Learning (FGL) enables privacy-preserving, distributed training of graph neural networks without sharing raw data. Among its approaches, subgraph-FL has become the dominant paradigm, with most work focused on improving overall node classification accuracy. However, these methods often overlook fairness due to the complexity of node features, labels, and graph structures. In particular, they perform poorly on nodes with disadvantaged properties, such as being in the minority class within subgraphs or having heterophilous connections (neighbors with dissimilar labels or misleading features). This reveals a critical issue: high accuracy can mask degraded performance on structurally or semantically marginalized nodes. To address this, we advocate for two fairness goals: (1) improving representation of minority class nodes for class-wise fairness and (2) mitigating topological bias from heterophilous connections for topology-aware fairness. We propose FairFGL, a novel framework that enhances fairness through fine-grained graph mining and collaborative learning. On the client side, the History-Preserving Module prevents overfitting to dominant local classes, while the Majority Alignment Module refines representations of heterophilous majority-class nodes. The Gradient Modification Module transfers minority-class knowledge from structurally favorable clients to improve fairness. On the server side, FairFGL uploads only the most influenced subset of parameters to reduce communication costs and better reflect local distributions. A cluster-based aggregation strategy reconciles conflicting updates and curbs global majority dominance . Extensive evaluations on eight benchmarks show FairFGL significantly improves minority-group performance , achieving up to a 22.62 percent Macro-F1 gain while enhancing convergence over state-of-the-art baselines.

Federated Prototype Graph Learning

In recent years, Federated Graph Learning (FGL) has gained significant attention for its distributed training capabilities in graph-based machine intelligence applications, mitigating data silos while offering a new perspective for privacy-preserve large-scale graph learning. However, multi-level FGL heterogeneity presents various client-server collaboration challenges: (1) Model-level: The variation in clients for expected performance and scalability necessitates the deployment of heterogeneous models. Unfortunately, most FGL methods rigidly demand identical client models due to the direct model weight aggregation on the server. (2) Data-level: The intricate nature of graphs, marked by the entanglement of node profiles and topology, poses an optimization dilemma. This implies that models obtained by federated training struggle to achieve superior performance. (3) Communication-level: Some FGL methods attempt to increase message sharing among clients or between clients and the server to improve training, which inevitably leads to high communication costs. In this paper, we propose FedPG as a general prototype-guided optimization method for the above multi-level FGL heterogeneity. Specifically, on the client side, we integrate multi-level topology-aware prototypes to capture local graph semantics. Subsequently, on the server side, leveraging the uploaded prototypes, we employ topology-guided contrastive learning and personalized technology to tailor global prototypes for each client, broadcasting them to improve local training. Experiments demonstrate that FedPG outperforms SOTA baselines by an average of 3.57\% in accuracy while reducing communication costs by 168x.

Toward General and Robust LLM-enhanced Text-attributed Graph Learning

Recent advancements in Large Language Models (LLMs) and the proliferation of Text-Attributed Graphs (TAGs) across various domains have positioned LLM-enhanced TAG learning as a critical research area. By utilizing rich graph descriptions, this paradigm leverages LLMs to generate high-quality embeddings, thereby enhancing the representational capacity of Graph Neural Networks (GNNs). However, the field faces significant challenges: (1) the absence of a unified framework to systematize the diverse optimization perspectives arising from the complex interactions between LLMs and GNNs, and (2) the lack of a robust method capable of handling real-world TAGs, which often suffer from texts and edge sparsity, leading to suboptimal performance. To address these challenges, we propose UltraTAG, a unified pipeline for LLM-enhanced TAG learning. UltraTAG provides a unified comprehensive and domain-adaptive framework that not only organizes existing methodologies but also paves the way for future advancements in the field. Building on this framework, we propose UltraTAG-S, a robust instantiation of UltraTAG designed to tackle the inherent sparsity issues in real-world TAGs. UltraTAG-S employs LLM-based text propagation and text augmentation to mitigate text sparsity, while leveraging LLM-augmented node selection techniques based on PageRank and edge reconfiguration strategies to address edge sparsity. Our extensive experiments demonstrate that UltraTAG-S significantly outperforms existing baselines, achieving improvements of 2.12\% and 17.47\% in ideal and sparse settings, respectively. Moreover, as the data sparsity ratio increases, the performance improvement of UltraTAG-S also rises, which underscores the effectiveness and robustness of UltraTAG-S.

GraphMaster: Automated Graph Synthesis via LLM Agents in Data-Limited Environments

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.