Beyond Feature and Structure Alignment: Learning Transferable Propagation Knowledge for Graph Foundation Models

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for enabling knowledge transfer across diverse domains. Unlike traditional graph learning methods that are typically designed for in-domain settings, GFMs aim to learn transferable knowledge that can generalize to unseen graph domains. However, unlike language or visual data, graphs lack intrinsic and unified representation units, such as tokens in language and patches in vision, making it challenging to identify transferable knowledge units for building graph foundation models. Existing graph foundation models mainly focus on mitigating domain discrepancies through feature alignment and structure alignment, while overlooking the exploration of transferable knowledge units underlying graph data. Moreover, these methods generally rely on fixed propagation mechanisms during message passing, overlooking the heterogeneity in propagation patterns, as different edges may exhibit distinct propagation patterns for different feature dimensions. To address these limitations, we propose a Propagation-aware Graph Foundation Model (ProGFM), which regards the propagation relationships between edges and feature dimensions as transferable knowledge units. Through a propagation relationship prototype bank, ProGFM learns cross-domain transferable propagation knowledge, enabling adaptive information aggregation in unseen graph domains. Extensive experiments across various cross-domain transfer scenarios demonstrate that ProGFM possesses strong cross-domain knowledge transfer capability and exhibits superior generalization performance compared with existing methods.

What Makes Graph Unified? Principles and Generative Sliding-Window Transformer for Graph Foundation Models

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for general-purpose graph learning, aiming to learn reusable knowledge that generalizes across diverse graph domains and downstream tasks, reducing the need for specific model development. Achieving this goal requires reconciling the substantial heterogeneity in node features, graph structures, and semantic information across domains. Among them, heterogeneous node features constitute a fundamental input-level barrier, as their dimensionality and semantics vary substantially across datasets. Existing studies typically project or map heterogeneous node features into a fixed-dimensional space, often implicitly equating dimensional uniformity with effective feature unification. Yet dimensional consistency alone does not ensure that the unified features preserve informative semantics and capture transferable patterns that can support cross-domain knowledge transfer. To bridge this conceptual gap, we distill four desiderata for cross-domain graph feature unification: formal uniformity, cross-domain transferability, information preservation, and backbone compatibility. Guided by these principles, we propose SliGFM, a graph foundation model built upon topology-aware sliding-window feature encoding and generative reconstruction. SliGFM orders feature dimensions by topological smoothness and scans the reordered features with a shared sliding-window feature encoder, transforming heterogeneous features into a common space of ordered fixed-dimensional feature tokens. This formulation enables a smoothness-aware transformer to capture transferable relational patterns among feature tokens within each node, while the generative reconstruction objective encourages preservation of the original feature information.

AgentGFM: A Graph Foundation Model with Node-Agent Information-Flow Control

Graph Foundation Models (GFMs) aim to learn transferable knowledge from multi-domain graphs and adapt to unseen scenarios. As a fundamental source of relational semantics in graphs, the transferability of topological patterns has long been central to GFM research. However, local structural patterns may vary across graphs and even among nodes within the same graph. Despite such structural variation, most existing GFMs rely on manually designed propagation schemes and apply them to new graphs largely unchanged. Such fixed schemes may not suit the diverse structural patterns of different nodes. This raises a key question: can each node autonomously determine how information should be propagated through the graph? We refer to this capability as information-flow control. Inspired by recent advances in agent technology, we formulate this problem as agent-based decision making and treat each node as an agent. Accordingly, we propose AgentGFM, in which all node agents follow a shared end-to-end trainable policy rather than using independent models. For adaptive information-flow control, each node interacts with the graph through a predict-act-observe-correct process. During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting. The resulting observation is compared with the prediction and their discrepancy is used to correct the node state and guide subsequent interactions. Extensive experiments across node-level, graph-level and large-scale transfer scenarios demonstrate the effectiveness of AgentGFM across diverse graph topologies.

CHARM: A Multimodal Graph Foundation Model with Hierarchical Context Modeling for Zero-Shot Transfer

Graph foundation models (GFMs) have emerged as a promising paradigm for transferring knowledge across graph domains and tasks. Real-world graphs associate nodes with text, images, and other modalities, making multimodal graphs essential for representing complex entities and relations. Moreover, collecting labels and adapting models for every new graph domain is costly and often infeasible, motivating zero-shot transfer. Unfortunately, zero-shot transfer on multimodal graphs remains underexplored. Existing GNN-based graph foundation models typically require downstream adaptation, whereas LLM-based graph methods mainly address unimodal graphs or tasks within a single domain. This setting presents two key challenges. First, models must generalize knowledge from individual modalities while capturing transferable cross-modal relations. Second, without target-domain fine-tuning, node representations remain entangled with domain-specific structures and modality-specific characteristics, obscuring shared concepts in unseen domains. To address these challenges, we propose CHARM, a multimodal graph foundation model with hierarchical context modeling for zero-shot transfer. CHARM replaces isolated raw nodes with hierarchical graph contexts that capture multimodal semantics and cross-modal relations. These contexts map domain-specific node patterns to shared high-level concepts, reducing reliance on target-domain supervision or adaptation. A modality-aware graph context encoder integrates multimodal information with graph structure and converts the resulting representations into graph tokens for a large language model . Experiments show consistent improvements on zero-shot multimodal graph tasks.

Revisiting Positive Samples in Graph Contrastive Learning: From the Perspective of Message Passing

Graph Contrastive Learning (GCL), which trains graph encoders by maximizing similarity between positive samples and minimizing it between negative ones, has emerged as a mainstream graph pre-training paradigm. It is widely recognized that positive samples are essential in GCLs. Ideally, maximizing the similarity of positive samples enables graph encoders to capture intrinsic semantic and patterns of graph data. However, we discover an interesting phenomenon: GCLs can achieve competitive performance even without positive samples. This motivates us to revisit the fundamental mechanism of positive samples in GCLs. From the perspective of Dirichlet energy, we theoretically finds that message passing, a key mechanism in graph encoders, trivializes the maximization of positive samples, preventing GCLs from effectively learning from positive samples. To address this, we propose SPGCL to mitigate the trivialization caused by message passing and restore the learning efficacy of positive samples. Specifically, we find that high Dirichlet energy features help positive samples provide effective learning signals while low Dirichlet energy features contribute little to positive learning signal but is useful for positive sampling. Based on this, SPGCL propagates only high Dirichlet energy features and uses low energy features to construct a probability matrix for reliable positive sampling. Extensive experiments demonstrate the effectiveness of SPGCL.

A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation

Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks. Unlike text and images, graphs lack a shared vocabulary or regular spatial grid, making cross-graph transfer challenging. This challenge comes from both feature discrepancies and, more critically, diverse graph structures. Existing GFMs mainly improve transferability by unifying feature spaces or incorporating structural tokens and vocabularies. However, existing topology-aware designs still have limitations. Structural tokens are usually discrete, while structural vocabularies often rely on predefined substructures such as trees and cycles, whose limited coverage may miss richer relational patterns across graphs. Moreover, graph signals contain both high-frequency local patterns and smoother low-frequency patterns, which require different propagation behaviors. These components are often entangled in raw graph signals, while this spectral perspective is rarely explored in existing GFMs. To address these challenges, we propose SPG, a graph foundation model with spectral parsing and prototype-guided spatial propagation. SPG applies learnable Chebyshev filters to decompose node features into multiple spectral responses, reducing the mismatch between frequency-specific graph signals and propagation behaviors. It then constructs a Gromov-Wasserstein prototype geometry to distill transferable pairwise relations beyond predefined substructures into a shared structural space. The learned prototype geometry is further projected back as a prototype-guided propagation operator. Experiments demonstrate consistent improvements in cross-domain generalization.

LEDA: Latent Semantic Distribution Alignment for Multi-domain Graph Pre-training

Recent advances in generic large models, such as GPT and DeepSeek, have motivated the introduction of universality to graph pre-training, aiming to learn rich and generalizable knowledge across diverse domains using graph representations to improve performance in various downstream applications. However, most existing methods face challenges in learning effective knowledge from generic graphs, primarily due to simplistic data alignment and limited training guidance. The issue of simplistic data alignment arises from the use of a straightforward unification for highly diverse graph data, which fails to align semantics and misleads pre-training models. The problem with limited training guidance lies in the arbitrary application of in-domain pre-training paradigms to cross-domain scenarios. While it is effective in enhancing discriminative representation in one data space, it struggles to capture effective knowledge from many graphs. To address these challenges, we propose a novel Latent sEmantic Distribution Alignment (LEDA) model for universal graph pre-training. Specifically, we first introduce a dimension projection unit to adaptively align diverse domain features into a shared semantic space with minimal information loss. Furthermore, we design a variational semantic inference module to obtain the shared latent distribution. The distribution is then adopted to guide the domain projection, aligning it with shared semantics across domains and ensuring cross-domain semantic learning. LEDA exhibits strong performance across a broad range of graphs and downstream tasks. Remarkably, in few-shot cross-domain settings, it significantly outperforms in-domain baselines and advanced universal pre-training models.

MUG: Meta-path-aware Universal Heterogeneous Graph Pre-Training

Universal graph pre-training has emerged as a key paradigm in graph representation learning, offering a promising way to train encoders to learn transferable representations from unlabeled graphs and to effectively generalize across a wide range of downstream tasks. However, recent explorations in universal graph pre-training primarily focus on homogeneous graphs and it remains unexplored for heterogeneous graphs, which exhibit greater structural and semantic complexity. This heterogeneity makes it highly challenging to train a universal encoder for diverse heterogeneous graphs: (i) the diverse types with dataset-specific semantics hinder the construction of a unified representation space; (ii) the number and semantics of meta-paths vary across datasets, making encoding and aggregation patterns learned from one dataset difficult to apply to others. To address these challenges, we propose a novel Meta-path-aware Universal heterogeneous Graph pre-training (MUG) approach. Specifically, for challenge (i), MUG introduces a input unification module that integrates information from multiple node and relation types within each heterogeneous graph into a unified representation.This representation is then projected into a shared space by a dimension-aware encoder, enabling alignment across graphs with diverse schemas.Furthermore, for challenge (ii), MUG trains a shared encoder to capture consistent structural patterns across diverse meta-path views rather than relying on dataset-specific aggregation strategies, while a global objective encourages discriminability and reduces dataset-specific biases. Extensive experiments demonstrate the effectiveness of MUG on some real datasets.

GP2F: Cross-Domain Graph Prompting with Adaptive Fusion of Pre-trained Graph Neural Networks

Graph Prompt Learning (GPL) has recently emerged as a promising paradigm for downstream adaptation of pre-trained graph models, mitigating the misalignment between pre-training objectives and downstream tasks. Recently, the focus of GPL has shifted from in-domain to cross-domain scenarios, which is closer to the real world applications, where the pre-training source and downstream target often differ substantially in data distribution. However, why GPLs remain effective under such domain shifts is still unexplored. Empirically, we observe that representative GPL methods are competitive with two simple baselines in cross-domain settings: full fine-tuning (FT) and linear probing (LP), motivating us to explore a deeper understanding of the prompting mechanism. We provide a theoretical analysis demonstrating that jointly leveraging these two complementary branches yields a smaller estimation error than using either branch alone, formally proving that cross-domain GPL benefits from the integration between pre-trained knowledge and task-specific adaptation. Based on this insight, we propose GP2F, a dual-branch GPL method that explicitly instantiates the two extremes: (1) a frozen branch that retains pre-trained knowledge, and (2) an adapted branch with lightweight adapters for task-specific adaptation. We then perform adaptive fusion under topology constraints via a contrastive loss and a topology-consistent loss. Extensive experiments on cross-domain few-shot node and graph classification demonstrate that our method outperforms existing methods.

One Prompt Fits All: Universal Graph Adaptation for Pretrained Models

Graph Prompt Learning (GPL) has emerged as a promising paradigm that bridges graph pretraining models and downstream scenarios, mitigating label dependency and the misalignment between upstream pretraining and downstream tasks. Although existing GPL studies explore various prompt strategies, their effectiveness and underlying principles remain unclear. We identify two critical limitations: (1) Lack of consensus on underlying mechanisms: Despite current GPLs have advanced the field, there is no consensus on how prompts interact with pretrained models, as different strategies intervene at varying spaces within the model, i.e., input-level, layer-wise, and representation-level prompts. (2) Limited scenario adaptability: Most methods fail to generalize across diverse downstream scenarios, especially under data distribution shifts (e.g., homophilic-to-heterophilic graphs). To address these issues, we theoretically analyze existing GPL approaches and reveal that representation-level prompts essentially function as fine-tuning a simple downstream classifier, proposing that graph prompt learning should focus on unleashing the capability of pretrained models, and the classifier adapts to downstream scenarios. Based on our findings, we propose UniPrompt, a novel GPL method that adapts any pretrained models, unleashing the capability of pretrained models while preserving the structure of the input graph. Extensive experiments demonstrate that our method can effectively integrate with various pretrained models and achieve strong performance across in-domain and cross-domain scenarios.