When Do Graph Foundation Models Transfer? A Data-Centric Theory

• URL: http://arxiv.org/abs/2605.29828v1
• Date: Thu, 28 May 2026 12:07:27 GMT
• Title: When Do Graph Foundation Models Transfer? A Data-Centric Theory
• Abstract summary: 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.<n>We show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift.<n>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.
• Score: 68.54337055801571
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Directed Graph Topology Inference via Graph Filter Identification [54.541275287889164]
  We address the problem of inferring a directed network from nodal measurements generated by a graph convolutional filter.<n>A joint graph filter and topology identification algorithm is also proposed, which alternates between the aforementioned steps to offer improved sample complexity.
  arXiv  Detail & Related papers  (2026-06-25T18:25:57Z)
• A Graph Foundation Model with Spectral Parsing and Prototype-Guided Spatial Propagation [30.922981803680518]
  Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks.<n>This challenge comes from both feature discrepancies and, more critically, diverse graph structures.<n>Existing GFMs mainly improve transferability by unifying feature spaces or incorporating structural tokens and vocabularies.<n>We propose SPG, a graph foundation model with spectral parsing and prototype-guided spatial propagation.
  arXiv  Detail & Related papers  (2026-06-02T08:27:03Z)
• Rethinking Feature Alignment in Generalist Graph Anomaly Detection: A Relational Fingerprint-based Approach [60.199985286210904]
  Generalist graph anomaly detection (GAD) aims to detect anomalies on unseen graphs without graph-specific retraining.<n>Existing approaches primarily focus on aligning heterogeneous data across domains, which ignores different feature semantics.<n>We propose Fingerprint-based generalist GAD approach (ReFi-GAD)<n>We show that ReFi-GAD significantly outperforms state-of-the-art methods in experiments on 14 datasets.
  arXiv  Detail & Related papers  (2026-05-25T05:12:26Z)
• DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation [28.666612808886736]
  Graph domain adaptation (GDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph under distribution shifts.<n>Existing methods are largely feature-centric and overlook structural discrepancies, which become particularly detrimental under significant topology shifts.<n>We propose Dual-Aligned Structural Basis Distillation (DSBD) for GDA, a novel framework that explicitly models and adapts cross-domain structural variation.
  arXiv  Detail & Related papers  (2026-04-03T16:23:59Z)
• A Theory of Random Graph Shift in Truncated-Spectrum vRKHS [26.195791008324495]
  This paper develops a theory of graph classification under domain shift through a random-graph generative lens.<n>We consider intra-class graphs sharing the same random graph model (RGM) and the domain shift induced by changes in RGM components.
  arXiv  Detail & Related papers  (2026-02-27T10:19:57Z)
• Semantic Refinement with LLMs for Graph Representations [37.72134125261354]
  We propose a Data-Adaptive Semantic Refinement framework DAS for graph representation learning.<n>We evaluate our approach on both text-rich and text-free graphs.<n>Results show consistent improvements on structure-dominated graphs while remaining competitive on semantics-rich graphs.
  arXiv  Detail & Related papers  (2025-12-24T11:10:28Z)
• A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application [10.908840038943643]
  This paper proposes the unified extended matrix (UEM) framework, which integrates the extended-adjacency matrix and the unified graph representation matrix through parametric design.<n> Experimental results on synthetic and real-world datasets demonstrate that the UEM-GFT outperforms existing GSO-based methods in anomaly detection tasks.
  arXiv  Detail & Related papers  (2025-08-16T02:30:41Z)
• Invariant Graph Transformer for Out-of-Distribution Generalization [21.60139614144787]
  We introduce Graph Out-Of-Distribution generalized Transformer (GOODFormer)<n>It aims to learn generalized graph representations by capturing invariant relationships between predictive graph structures and labels.<n>We design an evolving subgraph positional and structural encoder to effectively and efficiently capture the encoding information of dynamically changing subgraphs.
  arXiv  Detail & Related papers  (2025-08-01T04:11:53Z)
• Supercharging Graph Transformers with Advective Diffusion [28.40109111316014]
  This paper proposes Advective Diffusion Transformer (AdvDIFFormer), a physics-inspired graph Transformer model designed to address this challenge.<n>We show that AdvDIFFormer has provable capability for controlling generalization error with topological shifts.<n> Empirically, the model demonstrates superiority in various predictive tasks across information networks, molecular screening and protein interactions.
  arXiv  Detail & Related papers  (2023-10-10T08:40:47Z)
• Stable and Transferable Hyper-Graph Neural Networks [95.07035704188984]
  We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs) We provide a framework for bounding the stability and transferability error of GNNs across arbitrary graphs via spectral similarity.
  arXiv  Detail & Related papers  (2022-11-11T23:44:20Z)
• Counterfactual Intervention Feature Transfer for Visible-Infrared Person Re-identification [69.45543438974963]
  We find graph-based methods in the visible-infrared person re-identification task (VI-ReID) suffer from bad generalization because of two issues. The well-trained input features weaken the learning of graph topology, making it not generalized enough during the inference process. We propose a Counterfactual Intervention Feature Transfer (CIFT) method to tackle these problems.
  arXiv  Detail & Related papers  (2022-08-01T16:15:31Z)
• Graph Spectral Embedding using the Geodesic Betweeness Centrality [76.27138343125985]
  We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and neighborhood proximity in a single representation.
  arXiv  Detail & Related papers  (2022-05-07T04:11:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.