Graph Transfer Learning

Graph foundation models aim to transfer across graphs, feature spaces, relational schemas, and prediction tasks, yet existing approaches typically generalize only within particular graph modalities or tasks. We propose Wander, a graph foundation model designed to operate across these settings within a single pretrained checkpoint. Following the prior-predictive perspective, we formulate graph learning as completion of a partially observed graph. We realize this task-general view through a common interface based on random walks, allowing the same model to operate across homogeneous and multi-relational graphs with varying features, labels, and relational schemas. Wander can increase its structural context at inference time without changing its learned parameters and, under suitable assumptions, universally approximates the corresponding Bayes-optimal predictor on bounded connected graphs. Empirically, a single pretrained checkpoint achieves state-of-the-art or highly competitive results across node classification, homogeneous link prediction, and knowledge-graph link prediction. Moreover, joint pretraining across graph modalities and tasks preserves performance in specialized settings while enabling positive transfer and the composition of separately learned capabilities at inference time.

Signed graphs arise in trust--distrust networks, financial correlation systems, biological interaction graphs, and many other domains in which edges can be positive or negative and may also be directed. While signed graph neural networks have improved task-specific learning, graph transfer learning on signed graphs remains underdeveloped. In this paper, we introduce TopoSIGN, a pioneer topology-guided graph pre-training and prompt learning framework for signed graphs. TopoSIGN combines a structural encoder built on the magnetic signed Laplacian with a novel persistent-homology branch that summarizes signed topology through Dowker-complex persistence images. The fused embeddings are then transferred to a prompt learning function. Experimental results on synthetic and real-world datasets demonstrate the efficacy of TopoSIGN in extracting useful structural information in signed graphs, as well as the adaptability and flexibility of the proposed general framework.

Knowledge graph foundation models such as ULTRA achieve zero-shot link prediction on unseen graphs through dedicated architectures that hard-code a transfer mechanism. In this work we move that mechanism out of the architecture and into the representation, by reifying the input graph: every fact becomes a node, connected to its subject, object, and relation type through a fixed vocabulary of six meta-relations, with relation types as anonymous shared nodes rather than model parameters. On this representation, five textbook GNNs (GAT, GINE with sum and with mean+max aggregation, GraphSAGE, R-GCN), each trained on a single knowledge graph of 4,245 triples for 30 minutes on one NVIDIA A100, transfer zero-shot to 40 inductive link-prediction benchmarks. The best of them, an off-the-shelf GAT, matches ULTRA, a dedicated foundation model pretrained on three graphs, across ULTRA's own evaluation suite. The same fixed vocabulary extends to relational databases, a row becoming an entity and a foreign-key column a relation type; a preliminary probe on two unseen databases, with no cell values, schema text or in-context labels, shows a model of this family pretrained on three knowledge graphs ranking foreign-key targets far above random-initialization and degree controls. We release the code, the checkpoints, and the evaluation pipeline for all 40 benchmarks.

This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs) operating on covariance matrices as graphs. Covariance matrices are ubiquitous across domains, and hence, the deployment of GNNs often leverages graphs of pairwise statistical dependencies. Existing theoretical contributions on GNNs consider abstract graph representations and cannot accommodate the data-driven nuances associated with covariance matrices. This tutorial brings into focus various novel theoretical insights via mathematical analyses of VNNs that have broad signal processing implications, including: (i) a conceptual equivalence between VNNs and principal component analysis (PCA)-based information processing; (ii) refined stability bounds on predictive outcomes in the presence of finite sample-induced covariance matrix perturbations; and (iii) refined characterization of transferability of VNNs across multiscale datasets. The theoretical insights discussed herein provide the underlying principles and justification towards adopting VNNs over workhorse PCA-based learning pipelines, in applications where covariance matrices are useful descriptors of data structure. We also convey how impact of these foundational advances permeates to principled designs and applications of learning methods across broad domains where covariance matrices emerge. Notably, we elucidate the conceptual insights facilitated by VNNs to the specific task of characterizing brain age gap for neurodegenerative conditions using neuroimaging datasets, a timely problem in computational neuroscience. Broader impacts to other application domains are discussed as well.

Designing foundation models for graphs is challenging due to the irregular structure of graphs and the different sizes and characteristics of embeddings. Chimaera integrates mixture-of-experts with graph foundation models (GFM). It integrates different GFM architectures, such as graph prompts and linear GNN models. Large language models are used to generate embeddings, and experts can be trained and combined following different strategies, GFMs, embeddings, etc. Furthermore, Chimaera extends existing linear GNNs to support link-level and graph-level tasks in addition to node-level tasks. Empirical analyses are performed on same-task and cross-task experiments with node, link, and graph classification tasks using six benchmark text-attributed graph datasets. The experiments demonstrate the effectiveness of Chimaera and its capabilities for transfer across tasks and datasets. Further insights include the need to use both large and small language models to generate embeddings for the experts, a strong cross-task transferability of simple but effective linear GNNs, and using few samples only to provide strong results.

Graph Neural Networks (GNNs) have emerged as a cornerstone for representing complex relational dependencies in diverse multimedia tasks, particularly in cross-platform user interest modeling and cross-modal semantic alignment. In the real world, a practical defense against graph adversarial perturbations is needed. However, we observe that the prevailing adversarial purification methods are essentially domain-restricted defenses, which leads to the following shortcomings: (1) single-domain data provides insufficient structural and semantic diversity for learning robust purification criteria; (2) training of domain-specific defense strategies from scratch consumes substantial computational cost. To address the above limitations, we propose a transferable graph purification scheme, named ProGAP, to bridge adversarial defense knowledge via vulnerability-aware graph prompt learning. Firstly, to capture universal adversarial patterns, a perturbation-capture edge detector is pretrained on data-rich graphs by jointly modeling topological and semantic information. Subsequently, to achieve more knowledge transfer w.r.t. robustness, vulnerability-aware prompts are designed that inject targeted purification guidance into biased nodes, during which the pretrained detector adapts to distribution shifts in downstream graphs without parameter-laborious updates. Experimental results demonstrate that compared with state-of-the-art baselines, our ProGAP achieves 1%-9% improvement, and reduces the time consumption by up to 2.2x. The code for ProGAP is available at https://github.com/Lieyoufffff/ProGAP.

Many real-world graphs support multiple predictive tasks over the same underlying structure, creating an opportunity to reuse supervision across node classification (NC) and link prediction (LP). However, existing evaluations often rely on incompatible splits, observed-graph assumptions, and negative sampling rules, making conclusions about same-graph cross-task transfer unreliable. We formalize same-graph NC-LP transfer and propose a leakage-free protocol that fixes node and edge splits, uses a shared message-passing graph that excludes evaluated edges, and employs fixed negatives for LP. Across three backbones (GCN, GraphSAGE, GPS), we find that transfer is strongly directional and predictable: NC $\to$ LP is consistently beneficial on homophilic graphs, while LP $\to$ NC is fragile and can even degrade accuracy under naive representation reuse. LP $\to$ NC becomes reliably positive mainly in a structure-dominant regime where LP is easy but NC is unsaturated, suggesting that LP acts as structural pretraining. Finally, we introduce the CoTask Score (CTS) to summarize joint NC+LP utility when a shared encoder must serve both tasks, and show that simple dataset statistics, especially homophily, can guide mechanism choice and help avoid negative transfer.

Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs. This raises a central question: when can a model trained on a smaller, scaled-down replica of a graph be deployed on the full-resolution graph without retraining? We introduce a zero-shot transfer protocol in which a GNN is trained on a graph coarse-grained by geometric renormalization (GR), and the resulting weights are transferred directly to the original network. Across synthetic and real-world networks, training on GR scaled-down replicas preserves much of the original-scale predictive performance while significantly reducing training cost. We further find that learned representations and predictive trajectories remain aligned across scales. These findings suggest that structural similarity may be more important than network size in determining GNN transferability, opening a path toward scale-equivariant graph architectures.

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.

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.

Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time. Physics-informed learning moves this cost to training, but uses a single encoder pathway whose latent geometry de-learns under fine-tuning and admits no quantitative transfer guarantee. We propose an asymmetric two-pathway architecture that resolves both issues. A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation; a student encoder learns the same latent geometry from sparse field data and operator descriptors. At deployment the teacher is discarded, and the frozen student runs in a single forward pass with a transfer certificate. The design connects to privileged-information learning, knowledge distillation, and cross-modal distillation, but targets cross-instance transfer rather than fixed-instance prediction: topology and operator may change, while the latent task does not. We establish sufficient and near-necessary transfer conditions via Wasserstein proximity between latent laws, yielding a zero-shot error bound, and develop a finite-sample certification protocol with active expansion when coverage is incomplete. The framework applies wherever a system admits an operator with reportable spectrum. On power-system estimation, it achieves zero-shot transfer to 100 unseen topologies, a 95% certificate pass rate, accuracy competitive with topology-aware Newton--Raphson, and sub-millisecond inference. These results suggest asymmetric pathways plus operator-anchored latent geometry provide a foundation for certified zero-shot inference and control.

Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation choices, we ask a data-centric question: which properties of two graph domains determine how much a fixed representation model changes its outputs? Using a graphon-based continuous limit for dense graphs, we show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift into (i) graph-specific finite-sample approximation terms and (ii) an intrinsic, relabeling-invariant domain discrepancy capturing structural mismatch. A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs. Experiments on synthetic and real graphs validate the theory and translate the decomposition into guidance for data curation in GFM transfer.

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.

Graph pre-training can facilitate knowledge transfer across graph datasets, but severe structural and feature shifts may cause negative transfer and adaptation-induced overwriting of reusable knowledge. We propose DIB-OD, a heterogeneous graph adaptation framework that combines a Decoupled Information Bottleneck with Online Distillation. A multiview teacher first learns a compressed, task-relevant representation, which is distilled into a transferable core branch and a complementary residual branch. Mutual-information objectives and HSIC-based dependence regularization discourage information overlap between the branches, while a confidence-aware semantic regularizer and a frozen teacher anchor reliable pretrained information during target-domain adaptation. Experiments on seven graph-classification datasets spanning chemical, biological, and social-network domains show consistent improvements over representative baselines, particularly under challenging cross-type transfer.

Graphs are a central representation in biomedical research, capturing molecular interaction networks, gene regulatory circuits, cell--cell communication maps, and knowledge graphs. Despite their importance, currently there is not a broadly reusable foundation model available for graph analysis comparable to those that have transformed language and vision. Existing graph neural networks are typically trained on a single dataset and learn representations specific only to that graph's node features, topology, and label space, limiting their ability to transfer across domains. This lack of generalization is particularly problematic in biology and medicine, where networks vary substantially across cohorts, assays, and institutions. Here we introduce a graph foundation model designed to learn transferable structural representations that are not specific to specific node identities or feature schemes. Our approach leverages feature-agnostic graph properties, including degree statistics, centrality measures, community structure indicators, and diffusion-based signatures, and encodes them as structural prompts. These prompts are integrated with a message-passing backbone to embed diverse graphs into a shared representation space. The model is pretrained once on heterogeneous graphs and subsequently reused on unseen datasets with minimal adaptation. Across multiple benchmarks, our pretrained model matches or exceeds strong supervised baselines while demonstrating superior zero-shot and few-shot generalization on held-out graphs. On the SagePPI benchmark, supervised fine-tuning of the pretrained backbone achieves a mean ROC-AUC of 95.5%, a gain of 21.8% over the best supervised message-passing baseline. The proposed technique thus provides a unique approach toward reusable, foundation-scale models for graph-structured data in biomedical and network science applications.