A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework
Multi-label node classification is an important yet challenging task in graph learning, where nodes exhibit multiple semantics simultaneously. Existing methods for multi-label node classification can effectively model multiple labels, while only considering in-domain scenarios where the model needs to be trained and tested within the same graph domain, resulting in limited cross-domain generalization. Recently, Graph Foundation Models (GFMs) have emerged as a promising paradigm for learning transferable graph representations across diverse graph domains and downstream tasks. However, existing GFMs are built upon single-label assumption, where all nodes are arbitrarily regarded as containing only one class of semantic and embedded into a single representation. For multi-label nodes, such a representation essentially approximates multiple semantics with a single point in the representation space, inevitably leading to semantic entanglement and making simultaneous discrimination of multiple labels difficult. To address these limitations, we propose a Multi-Semantic Basis Graph Foundation Model (MSB-GFM), a framework for cross-domain multi-label node classification. Specifically, we introduce a multi-semantic basis representation learning paradigm that models each multi-label node as an adaptive composition of semantic bases, thereby enabling flexible representational capacity for modeling multiple semantics. Furthermore, we develop a semantic-structure dual-channel architecture with domain adversarial training for effective cross-domain knowledge transfer. Extensive experiments demonstrate the effectiveness of our model.
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.
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.
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.
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.
A graph foundation model generalizes across graph domains by mapping every input into one shared representation before any task reasoning. We call this map the alignment layer, the component that separates a graph foundation model from a graph neural network, and we show it is a distinct attack surface that prior work has not studied. We attack it at inference time, with no access to training, on six public models spanning spectral tokenizers, text embedding spaces, and a discrete codebook. A directed representation-space perturbation collapses every model, but at a budget comparable to the representation norm a plain graph network also needs, with one exception: OpenGraph, whose spectral tokenizer collapses at a fifth of that budget, an alignment-specific fragility a plain network does not share and which a same-representation control traces to the tokenizer rather than the decoder. A realizable input-space attack that edits edges, features, or text removes at least half the correct predictions on three of the six models at peak. How much of this fragility an input-access attacker realizes tracks how directly the decoder reads the representation, and not the clean accuracy a task leaves; we measure this carrier gain structurally from the decoder's local Lipschitz sensitivity, and report clean-accuracy headroom as a within-model ordering heuristic that does not survive on realizable attacks.
Node representation learning has advanced rapidly, yet most existing methods rely on per-dataset training and hyperparameter tuning. This dataset-specific optimization comes from the difficulty of designing reusable graph models that generalize across diverse graph datasets. In this work, we introduce Node4All, a node representation learner applicable to arbitrary graph datasets without any dataset-specific optimization. Node4All is built on two complementary ideas. At the architectural level, we introduce the Channel Graph Transformer (CGT), which enables a single fixed parameterization to process arbitrary graph datasets. At the learning level, we propose a self-supervised learning based on a series of synthetic graphs. Together, these components enable generalization beyond individual datasets, which is infeasible with existing architectures and learning frameworks. We extensively evaluate Node4All on node classification across 25 benchmarks against 21 baselines, covering both supervised and self-supervised methods. Despite all baselines being trained and optimized for each dataset, a single Node4All, applied uniformly across the datasets, achieves a competitive ranking of 5th among 21 baselines. Moreover, Node4All supports one-shot and in-context learning with an appropriate predictor and outperforms recent graph foundation models (GFMs) in these settings. These results demonstrate that Node4All not only achieves reusability across arbitrary graph datasets, but also remains an effective solution in practice. Code and model checkpoints are available in https://github.com/dooho00/node4all.
Multimodal-attributed graphs (MAGs), whose nodes carry modalities such as images and text alongside topological structure, now pervade applications including social platforms, e-commerce, and biomedical networks, offering richer semantic signals than single-modality graphs. In practice, such graphs are fragmented across privacy-restricted silos owned by different platforms and institutions, so learning a broadly transferable model over them demands collaborative training that never exposes raw data. This places the task at the intersection of multimodal graph learning and federated learning, yet existing methods cover only one side of it. To address the challenges from these two perspectives, we propose FedGAMMA, casting federated multimodal graph foundation learning as a two-stage semantic-structural alignment problem of federated pre-training and prompt-based fine-tuning. During pre-training, a shared-private semantic enhancer disentangles cross-modal commonality from modality-specific information, aligning it through optimal transport, a topology-aware graph fusion module decouples semantic and structural views via semantic residual graphs and dual positional encodings, and a dual-channel affinity-aware aggregation mechanism estimates client similarity from feature and graph centroids without exposing raw data. During fine-tuning, FedGAMMA adapts the pretrained encoder through lightweight graph-aware prompts, a shared prompt pool with controlled exploration, and channel-wise prompt synchronization. Experiments on twelve multimodal graph datasets show FedGAMMA consistently surpassing a broad range of baselines across downstream tasks, with gains of up to 12.96%. FedGAMMA further outperforms competitive baselines accross multi-domain datasets on multiple tasks with up to 5.71% under few-shot learning scenario.
Multimodal graph foundation models aim to learn reusable knowledge from graphs enriched with text, images, attributes, and relational topology, thereby supporting diverse graph-centric and modality-centric tasks. In practice, however, such multimodal graphs are often distributed across decentralized clients, where raw contents and local structures cannot be centrally shared due to privacy constraints. This motivates federated multimodal graph foundation learning, which requires not only transferable representation learning but also intrinsic semantic traceability under strict data isolation. Existing methods usually exchange or store knowledge through parameters, prototypes, embeddings, or compact codebooks, which support optimization and transfer but do not explicitly expose how modality evidence, node semantics, and topology context jointly support predictions. To bridge this gap, we propose FedLAB, a traceable semantic codebook framework that organizes multimodal graph knowledge into typed hierarchical codebooks for modality evidence, node semantics, and topology context. FedLAB further refines these trace units through federated semantic barycenter pre-training while keeping raw multimodal contents and graph structures local. Extensive experiments on 10 benchmarks and 6 downstream tasks show that FedLAB improves over state-of-the-art baselines by up to 7.53\%, while preserving a native semantic trace interface.
Michał Czuba, Mateusz Stolarski, Adam Piróg +2cs.LG cs.SI
Network dynamics - including spreading, influence maximisation, and epidemic modelling - remain largely confined to the transductive paradigm, where models are trained on a single network and cannot be reused on unseen graphs without retraining. We argue that inductive cross-network generalisation is a necessary prerequisite for Graph Foundation Models (GFMs) in this domain and propose four design properties towards this goal. As a proof of concept, ts-net (TopSpreadersNetwork), trained solely on synthetic multilayer networks (MLNs), demonstrates zero-shot generalisation to real-world MLNs of varying size and layer count, outperforming classical heuristics and transductive baselines on three of four metrics. Based on ts-net's performance, we further outline five open challenges towards building GFMs for network dynamics: scale, many-layer generalisation, self-supervised pretraining, cross-task transfer, and node-attribute integration.
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.
Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabilities of GFMs. Specifically, the introduced Hyperbolic Knowledge Indexing module retains the tree-like hierarchies of the external knowledge base by modeling them within hyperbolic space. The Multi-granularity Retrieval module then provides GFMs with the global semantic anchors and local semantic nuances through coarse-grained and fine-grained knowledge retrieval, respectively. Finally, the Dual-path Fusion module achieves effective knowledge integration for graph tasks at both the feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in the zero-shot setting, highlighting the generalization of our method for robust GFMs inference.
Graph Foundation Models (GFMs), built upon the Pre-training and Adaptation paradigm, have emerged as a research hotspot in graph learning. For GNN-based GFMs, graph prompt tuning has become the prevailing adaptation method for downstream tasks. Although recent methods explain why graph prompt tuning works, how to rigorously measure its adaptation capacity remains an open problem. Addressing this problem is critical for understanding the capability limits of graph prompt tuning and for developing more powerful adaptation methods. In this paper, we propose Prismatic Space Theory (PS-Theory), a novel mathematical framework to quantify the capacity of adaptation methods, while focusing on establishing the upper bound for the adaptation capacity of graph prompt tuning. Building upon the proposed PS-Theory, we further introduce Message Tuning for GFMs (MTG), a lightweight approach that injects a small set of learnable message prototypes into each layer of the GNN backbone to adaptively guide message fusion without updating pre-trained weights. Through our PS-Theory, we prove that the adaptation capacity of MTG can exceed the theoretical upper bound of graph prompt tuning. Extensive experiments demonstrate that MTG consistently outperforms graph prompt baselines across diverse benchmark datasets, providing strong empirical support for our theoretical findings.
Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework called Neural Vector Bundle, which enables parsing intrinsic geometry with local coordinates. Building on this, we design GAUGE, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.
Moshe Eliasof, Krishna Sri Ipsit Mantri, Beatrice Bevilacqua +2cs.LG
Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.