Graph Foundation Models

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9 papers in the last four weeks, up 200% on the four weeks before. 0.1% of all new papers.

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Latest papers 69

Jun 30, 2026cs.LG

FedLAB: Traceable Semantic Codebooks for Federated Multimodal Graph Foundation Learning

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.

Zekai Chen, Kairui Yang, Xuaner Chen +4

Beijing Institute of Technology, Beijing, China

Multimodal Federated Learning Representation Learning Federated Graph Learning Graph Foundation Models Multimodal Foundation Models Multimodal Model Interpretability

Jun 23, 2026cs.LG

A Fair Evaluation of Graph Foundation Models for Node Property Prediction

Due to the wide use of graph-structured data in different fields of industry and science, the development of Graph Foundation Models (GFMs) has recently attracted a lot of attention. While many different types of models are called GFMs, particular interest has been paid to GFMs designed for node property prediction tasks, which is one of the most popular settings in Graph ML with lots of real-world applications from fraud detection in financial and social networks to recommendation systems for e-commerce and user-generated content platforms. While a number of GFMs for this task have been recently proposed, the field has not converged to a unified evaluation setting, and different works evaluate their models in widely different ways, preventing reliable comparison of GFMs with each other and with other types of models. In this work, we conduct a fair and rigorous reevaluation of 9 recent GFMs for node property prediction, comparing them to strong Graph Neural Network (GNN) baselines. We find that, among these GFMs, only the most recent ones based on the Prior-data Fitted Networks paradigm outperform well-tuned GNNs in predictive performance, although at a higher inference cost.

Oleg Platonov, Gleb Bazhenov, Dmitry Eremeev +1

1HSE University · 2Yandex Research

Graph Neural Networks Graph Foundation Models Prior-Data Fitted Networks Node Classification

Jun 21, 2026cs.LG

Adaptive Recurrent Message Passing for Test Time Computing on Graphs

Pre-trained foundation models have demonstrated remarkable success in many domains, enabling a unified backbone to generalize across diverse downstream tasks. However, extending this paradigm to graph learning remains challenging due to the intrinsic mismatch between graph data and fixed architectural designs. In this work, we show that this limitation can be overcome via recurrent graph models. To achieve this, we conduct a systematic theoretical analysis, rigorously deriving step dependence as a necessary and sufficient condition for an adaptively convergent recurrent process. Building on this foundation, we propose AdaR, an Adaptive Recurrent graph model, empowering flexible test-time computing on various downstream tasks without changing model parameters. To enable adaptive inference, AdaR explicitly encodes normalized step information and representation-target relations into the recurrent updates. To ensure convergence of the recurrent process, AdaR employs gradient-based supervision signals that guide representation updates throughout the recurrence. Empirical results demonstrate that AdaR consistently outperforms strong baselines in both inductive and transductive settings.

Junshu Sun, Wanxing Chang, Qingming Huang +1

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · DAMO Academy, Alibaba Group, Hangzhou, China.

Adaptive Inference Graph Neural Networks Graph Foundation Models

Jun 16, 2026cs.LG

Half a Link can Be Enough to Predict a Whole Link: Understanding Generalization in Knowledge Graph Foundation Models

Knowledge graph (KG) foundation models (KGFMs) are zero-shot generalizers: trained once, they can predict links on unseen graphs without retraining. However, understanding when and how they can robustly generalize across KGs is still an open question. In this paper, we shed some light on their generalization mechanisms highlighting how their performance on unseen KGs is not uniform when it comes to partially seen links, which we call half-links. In fact, we show that to predict a test triple

(h,r,t)

it might suffice in practice to have observed the half-link

(h,r)

or

(r,t)

in the inference graph. This yields a taxonomy of four scenarios when combinations of these half-links are observed or not. In a rigorous stratified analysis over these scenarios, we reveal that SoTA KGFMs use seen half links for predictions, while unseen half-links pose different challenges. As such, our finer-grained taxonomy can be a diagnostic protocol for robust KGFM generalization and highlights where novel KGFMs can improve.

Cosimo Gregucci, Obaidah Theeb, Daniel Hernandez +2

Institute for AI, University of Stuttgart · University of Edinburgh · University of Southampton

Cross-Domain Generalization Graph Foundation Models KG Completion

Jun 16, 2026cs.LG

Handling Feature Heterogeneity with Learnable Graph Patches

In recent years, the rapid development of foundation models and graph pre-training technologies has spurred increasing interest in constructing a universal pre-trained graph model or Graph Foundation Model (GFM). However, a significant challenge is that existing models are unable to address feature heterogeneity in graph data without textual information, which hinders the transferability of graph models across different datasets. To bridge this gap, we propose the concept of learnable graph patches, which we regard as the smallest semantic units of any graph data. We decompose the graph into learnable graph patches by unfolding the node features and constructing corresponding patch structures separately. We then design a framework that mines transferable information from graph data across domains. Specifically, after extracting graph patches, we propose a patch encoder to extract knowledge from each unit and a patch aggregator to learn how the units are combined into a whole. Due to its domain-agnostic nature, the model can be applied to downstream data across different domains. Furthermore, we analyze the connection between our method and existing graph models, as well as the transferability of the node embeddings it generates. Empirically, our method not only achieves the capability to use multi-domain graphs for pre-training, but also shows enhanced performance across various downstream datasets and tasks. Moreover, we observe consistent improvement in downstream performance as the volume of pre-training data increases.

Yifei Sun, Yang Yang, Xiao Feng +4

Zhejiang University Hangzhou, China · Huazhong University of Science and Technology Wuhan, China · Finvolution Group Shanghai, China

Graph Representation Learning Cross-Domain Transfer Learning Graph Foundation Models

Jun 6, 2026cs.LG

Towards Graph Foundation Models for Dynamics in Complex Networked Systems: Lessons from Super-Spreader Identification in Multilayer Networks

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.

Michał Czuba, Mateusz Stolarski, Adam Piróg +2

Department of Artificial Intelligence, Wrocław University of Science and Technology, Wrocław, Poland · Semantics, Warsaw, Poland

Dynamical Systems Graph Foundation Models Cross-Dataset Generalization

Jun 4, 2026cs.LG

The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning

Current evaluation practices in relational learning rely heavily on flat leaderboards that average performance across heterogeneous datasets, implicitly assuming a uniform underlying structure. We show that this assumption introduces systematic bias: it obscures geometry-dependent performance variations and can lead to misleading conclusions about model generalization. In this work, we identify intrinsic geometry as a key latent factor governing model effectiveness. We demonstrate that conventional aggregated metrics mask critical performance trade-offs that only become visible when datasets are stratified by their geometric properties. To address this issue, we introduce a curvature-stratified evaluation framework that partitions datasets into positive, negative, and near-zero curvature regimes. Our benchmark evaluates 18 representative models including Graph Convolutional Networks (GCNs), Graph Foundation Models (GFMs), and tabular learning methods across 14 datasets. We find that model rankings are highly stable within each curvature regime but shift significantly across regimes, indicating that performance is fundamentally geometry-dependent rather than universally transferable. Notably, we identify regimes where GFMs offer diminishing returns compared to geometry-aligned GNNs. Based on these findings, we propose a geometry-aware evaluation protocol that yields more reliable and interpretable comparisons than standard aggregated benchmarks. We release all code, curvature-stratified dataset splits, and evaluation tools to support reproducible and rigorous assessment of future relational learning methods. Code and datasets are provided in our project homepage: https://sirbabbage.github.io/CurvBench_HOME/.

Shuo Wang, Xiangyu Wang, Quanxin Wang +9

University of Electronic Science and Technology of China · Tsinghua University · Western University +1

Graph Neural Networks Graph Representation Learning Geometric Representation Learning Graph Foundation Models

Jun 4, 2026cs.CL

Harnessing Structural Context for Entity Alignment Foundation Models

Entity alignment (EA) aims to identify equivalent entities across heterogeneous knowledge graphs (KGs) and is a key component of knowledge fusion and cross-KG reasoning. The recent EA foundation model demonstrates that alignment knowledge, once pretrained, can be directly applied to diverse previously unseen KG pairs. However, it still underuses structural context in two places: cross-KG interaction is weak during encoding, and final candidate ranking still relies too heavily on coarse similarity. We address these limitations with ContextEA, an enhanced encoder-decoder framework for transferable EA. On the encoder side, we introduce a cross-KG interaction encoder that unifies the two KGs with anchor bridges and performs earlier relation-aware cross-graph propagation. On the decoder side, we introduce a structural calibration decoder that calibrates alignment scores with entity-level, neighborhood-level, relation-level, and anchor-aware structural evidence. This design strengthens both structural context construction and structural context exploitation while remaining lightweight. Experiments on 29 EA datasets in OpenEA, SRPRS, and DBP show consistent gains over strong transferable baselines. Notably, the pretrained ContextEA already surpasses the finetuned baselines on all three benchmark groups, demonstrating substantially stronger transfer to unseen KGs. These results suggest that explicitly harnessing structural context is an effective direction for improving EA foundation models.

Xingyu Chen, Yuanning Cui, Zequn Sun +1

State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · Nanjing University of Information Science and Technology, Nanjing, China · National Institute of Healthcare Data Science, Nanjing University, Nanjing, China

KG Embedding Cross-Domain Transfer Learning Graph Foundation Models

Jun 2, 2026cs.LG

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.

Ankang Yang, Jitao Zhao, Dongxiao He +3

School of Computer Science and Technology Tianjin University Tianjin, China · School of Artificial Intelligence Hebei University of Technology Tianjin, China · Department of Health Technology and Informatics Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University Kowloon, Hong Kong

Graph Neural Networks Cross-Domain Generalization Graph Foundation Models Spectral Graph Convolution

Jun 2, 2026cs.IR

Generalizing Graph Foundation Models via Hyperbolic Retrieval-Augmented Generation

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.

Yifan Jin, Qirui Ji, Bin Qin +4

Institute of Software, Chinese Academy of Sciences · University of Chinese Academy of Sciences · Beijing, China +1

Retrieval-Augmented Generation Graph Retrieval-Augmented Generation Domain Generalization Graph Foundation Models

Jun 2, 2026cs.LG

Message Tuning Outshines Graph Prompt Tuning: A Prismatic Space Perspective

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.

Yancheng Chen, Dun Ma, Shuai Zhang +6

Academy of Mathematics and Systems Science, Chinese Academy of Sciences · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · Institute of Information Engineering, Chinese Academy of Sciences +4

Prompt Tuning Graph Foundation Models Parameter-Efficient Fine-Tuning

Jun 2, 2026cs.LG

Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles

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.

Li Sun, Zhenhao Huang, Yiding Wang +3

Beijing University of Posts and Telecommunications, Beijing, China · North China Electric Power University, Beijing, China · University of Cambridge, Cambridge, UK +1

GNN Expressivity Geometric Representation Learning Transfer Learning Graph Foundation Models Riemannian Geometry

May 29, 2026cs.AI

GraphARC: A Comprehensive Benchmark for Graph-Based Abstract Reasoning

Relational reasoning lies at the heart of intelligence, but existing benchmarks are typically confined to formats such as grids or text. We introduce GraphARC, a benchmark for abstract reasoning on graph-structured data. GraphARC generalizes the few-shot transformation learning paradigm of the Abstraction and Reasoning Corpus (ARC). Each task requires inferring a transformation rule from a few input-output pairs and applying it to a new test graph, covering local, global, and hierarchical graph transformations. Unlike grid-based ARC, GraphARC instances can be generated at scale across diverse graph families and sizes, enabling systematic evaluation of generalization abilities. We evaluate state-of-the-art language models on GraphARC and observe clear limitations. Models can answer questions about graph properties but often fail to solve the full graph transformation task, revealing a comprehension-execution gap. Performance further degrades on larger instances, exposing scaling barriers. More broadly, by combining aspects of node classification, link prediction, and graph generation within a single framework, GraphARC provides a promising testbed for future graph foundation models.

Saku Peltonen, August Bøgh Rønberg, Andreas Plesner +1

ETH Zürich Zürich, Switzerland

LLM Reasoning with Graphs Synthetic Benchmark Generation Graph Foundation Models Graph Reasoning

May 28, 2026cs.LG

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

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.

Jiajun Zhu, Ying Chen, Peihao Wang +4

University of Texas at Austin · Arizona State University · Georgia Institute of Technology

Graph Representation Learning Cross-Domain Transfer Learning Graph Foundation Models

May 26, 2026cs.AI

Boosting Knowledge Graph Foundation Models via Enhanced Negative Sampling

Knowledge graphs (KGs) have become the core backbone of numerous downstream tasks such as question answering and recommender systems. However, despite all this, KGs are often very incomplete. To perform zero-shot knowledge graph completion in unseen KGs, which have different relational vocabularies from those used for pre-training, KG foundation models (KGFMs) receive a wide range of attention. Existing KGFMs often perform training using random negative triples, which are constructed by replacing the head or tail entity of a positive triple with a random entity. However, these negative triples are often constructed with limited quality, providing weak supervision for KGFM training. In this paper, we propose a simple yet effective adaptive negative sampling approach, KMAS, to enhance existing KGFMs. KMAS constructs hard negative triples through the updated relation embeddings generated from the existing KGFM's relation encoder. To further adaptively align with the evolving capability of the KGFM during the training process, KMAS adjusts the ratio of hard negative triples dynamically throughout the whole training process: after a warmup phrase, it increases the ratio linearly and then decreases linearly. Extensive experiments are conducted over 44 data sets. Experimental results demonstrate that our proposed negative sampling method can enhance many SOTA KGFMs without requiring excessive additional time or memory consumption.

Yinan Liu, Wenjin Xu, Zhiyuan Zha +2

Northeastern University Shenyang, China

KG Embedding Graph Foundation Models KG Completion

May 25, 2026cs.LG

MDGMIX: Boundary-Aware Subgraph Mixing for Multi-Domain Graph Pre-Training

Multi-domain graph pre-training is a crucial step in constructing foundational graph models with cross-domain generalization capabilities. However, existing methods predominantly rely on jointly training all source domain graphs, resulting in high computational costs. Furthermore, it remains unclear whether all source domain graph data contribute equally to effective transfer. This paper empirically reveals significant data redundancy in multi-domain graph pre-training. Based on this finding, we propose the Multi-domain Graph Pre-training Framework, MDGMIX, which combines boundary-aware subgraph mixing with hierarchical discrimination. By selecting boundary nodes to construct challenging mixed-domain subgraphs, MDGMIX employs coarse-grained domain discrimination and fine-grained domain decomposition losses to decouple shared patterns from domain-specific patterns. During adaptation, MDGMIX employs a lightweight prompt weighting mechanism to transfer source domain knowledge. Extensive experiments demonstrate that MDGMIX consistently outperforms strong baselines in few-shot classification tasks while exhibiting superior time and memory efficiency. The code is available at: https://github.com/zhengziyu77/MDGMIX.

Ziyu Zheng, Yaming Yang, Ziyu Guan +2

School of Computer Science and Technology, Xidian University, Xi’an, China · School of Artificial Intelligence, Xidian University, Xi’an, China

Cross-Domain Generalization Cross-Domain Transfer Learning Graph Foundation Models

May 22, 2026cs.LG

Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids

Fast and reliable optimal power flow (OPF) approximation is important for power system operation, yet heterogeneous OPF graph models are often evaluated either with architecture-specific implementations or on limited training corpora. This paper presents a large-scale heterogeneous graph-learning workflow, built on HydraGNN, for data-driven OPF surrogate modeling and graph foundation-model (GFM) development. The workflow preserves buses, generators, loads, shunts, alternating-current (AC) lines, transformers, and device-to-bus relations and provides a common implementation for distributed preprocessing, multi-graphics-processing-unit (GPU) training, hyperparameter optimization (HPO), and downstream adaptation. Using approximately three million heterogeneous graphs from ten Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms (PGLib-OPF) cases spanning 14 to 13,659 buses, we compare six heterogeneous graph neural network (GNN) families under a common HPO campaign on Frontier, resulting in two compact HeteroSAGE and HeteroHEAT models (~1.6-1.7 million parameters) that achieve the lowest observed validation MSE. Strong and weak scaling using up to 1,024 Frontier nodes show that 256 nodes (corresponding to 1,024 AMD MI250X GPUs) provides the best time-to-solution balance for the measured workload. Two downstream tasks evaluate task adaptation on the IEEE 118-bus case: a classification task to distinguish nominal operating conditions from artificially generated extreme-overload conditions and N-1 single-component-outage regression to predict bus voltage magnitude and phase angle. Partial fine-tuning provides the strongest balance between predictive performance and computational requirements.

Massimiliano Lupo Pasini, Yijiang Li, Kibaek Kim +1

Computational Sciences and Engineering Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, USA

Neural Surrogate Modeling Heterogeneous GNNs Optimal Power Flow Graph Foundation Models Constrained Optimization Power Systems

May 18, 2026cs.LG

S2Aligner: Pair-Efficient and Transferable Pre-Training for Sparse Text-Attributed Graphs

Pre-training on text-attributed graphs (TAGs) is central to building transferable graph foundation models, where LLM-as-Aligner methods align graph and text representations through the semantic knowledge of large language models. However, these methods usually assume that node texts provide sufficient and reliable supervision, an assumption often violated in real-world sparse TAGs. When textual anchors are missing, noisy, or uneven across domains, graph structures must be aligned with weak semantic evidence, leading to unreliable structure-semantics correspondence and sparsity-induced transfer bias. This paper presents S2Aligner, a sparsity-aware and structure-enhanced LLM-as-Aligner framework for graph-text pre-training on sparse TAGs. The key idea is to decouple semantic alignment from structural modeling, allowing topology-aware signals to enhance alignment without contaminating the shared semantic space. Specifically, S2Aligner decomposes graph-text representations into semantic and structural components, uses structure-oriented reconstruction with consistency control to inject reliable topology cues into text representations, and suppresses inconsistent structural signals under textual sparsity. Moreover, S2Aligner introduces sparsity-aware cross-domain risk balancing, which calibrates domain risks through a global-domain density ratio and downweights unreliable sparse samples via graph reliability estimation. Theoretical analysis shows that this objective reduces cross-domain generalization gaps by controlling domain risk discrepancy. Extensive experiments across diverse graph domains, sparsity levels, and downstream tasks demonstrate that S2Aligner consistently outperforms existing baselines.

Yuhan Wang, Haopeng Zhang, Yibo Ding +6

Beihang University, Beijing, China · Tianjin University, Tianjin, China

Cross-Modal Alignment Text-Attributed Graph Learning Cross-Domain Transfer Learning Graph Foundation Models

May 15, 2026cs.DB

Towards Foundation Models for Relational Databases with Language Models and Graph Neural Networks

Relational databases store much of the world's structured information, and they are essential for driving complex predictive applications. However, deep learning progress on relational data remains limited, as conventional approaches flatten databases into single tables via manual feature engineering, discarding relational context. Relational deep learning (RDL) addresses this by modeling databases as relational entity graphs (REGs) for graph neural networks (GNNs), but remains task- and database-specific. To combine the strengths of both paradigms, we propose a hybrid architecture combining a fine-tuned BART encoder to capture intra-row semantics with a GraphSAGE-based GNN over REGs to inject relational context. Experiments on RelBench show that the GNN substantially enriches BART's row embeddings, achieving a ROC-AUC of 67.40 on the driver-dnf task from the rel-f1 dataset. This performance is competitive with supervised baselines such as LightGBM (68.86) and narrows the gap to RDL (72.62) to within 5.22 points, though a substantial gap remains to state-of-the-art foundation models such as KumoRFM (82.63). These results suggest that lightweight hybrid LM-GNN architectures offer a promising and resource-efficient path towards foundation models for relational databases.

Jingcheng Wu, Ratan Bahadur Thapa, Mojtaba Nayyeri +4

University of Stuttgart, Stuttgart, Germany · Web and Internet Science Research Group, University of Southampton, Southampton, United Kingdom

Relational Foundation Models Tabular Foundation Models Graph Neural Networks Graph Foundation Models Relational Deep Learning Relational Databases

May 14, 2026cs.LG

Controllable Molecular Generative Foundation Models

Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability. While reinforcement learning (RL) offers a natural post-training mechanism for task-specific optimization, applying it to graph generative models is hindered by the vast atom-wise action spaces and chemically invalid intermediate states. We propose \textbf{Co}ntrollable \textbf{Mole}cular Generative Foundation Models (CoMole), built with a unified motif-aware graph diffusion pipeline. By learning a motif-aware graph space, CoMole transfers pretrained structural priors into controllable generation, where RL optimizes conditional reverse policies over chemically meaningful decisions. We theoretically characterize the bottleneck of atom-level RL and justify motif-aware policy optimization. Across three heterogeneous benchmarks spanning materials and drug discovery, CoMole ranks first in controllability on all nine targets, reduces MAE by up to 48.2% relative to the strongest baselines, and maintains validity above 0.94 without rule-based correction or post-hoc filtering. We further show that CoMole transfers controllability to unseen properties by optimizing only task embeddings with the generator frozen, achieving performance competitive with strong task-specific baselines.

Yihan Zhu, Yuhan Liu, Weijiang Li +2

University of Notre Dame

Molecular Optimization Molecular Graph Generation Graph Foundation Models RL for Diffusion Models Molecular Generation Conditional Generative Modeling

May 14, 2026cs.AI

KGPFN: Unlocking the Potential of Knowledge Graph Foundation Model via In-Context Learning

Knowledge graph (KG) foundation models aim to generalize across graphs with unseen entities and relations by learning transferable relational structure. However, most existing methods primarily emphasize relation-level universality, while in-context learning, the other pillar of foundation models remains under-explored for KG reasoning. In KGs, context is inherently structured and heterogeneous: effective prediction requires conditioning on the local context around the query entities as well as the global context that summarizes how a relation behaves across many instances. We propose KGPFN, a KG foundation model using Prior-data Fitted Network that unifies transferable relational regularities with inference-time in-context learning from structured context. KGPFN first learns relation representations via message passing on relation graphs to capture cross-graph relational invariances. For query-specific reasoning, it encodes local neighborhoods using a multi-layer NBFNet as local context. To enable ICL at global scale, it constructs relation-specific global context by retrieving a large set of instances of the query relation together with their local neighborhoods, and aggregates them within a Prior-Data Fitted Network framework that combines feature-level and sample-level attention. Through multi-graph pretraining on diverse KGs, KGPFN learns when to instantiate reusable patterns and when to override them using contextual evidence. Experiments on 57 KG benchmarks demonstrate that KGPFN achieves strong adaptation to previously unseen graphs through in-context learning alone, consistently outperforming competitive fine-tuned KG foundation models. Our code is available at https://github.com/HKUST-KnowComp/KGPFN.

Yisen Gao, Jiaxin Bai, Haoyu Huang +5

Department of Computer Science and Engineering, HKUST, Hong Kong, China · Department of Computer Science and Engineering, HKBU, Hong Kong, China

Graph Neural Networks In-Context Learning Graph Foundation Models KG Completion

May 14, 2026cs.LG

GFMate: Empowering Graph Foundation Models with Test-time Prompt Tuning

Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.

Yan Jiang, Ruihong Qiu, Zi Huang

School of Electrical Engineering and Computer Science, The University of Queensland, Brisbane, Queensland, Australia

Domain Adaptation Prompt Tuning Graph Foundation Models Test-Time Prompt Tuning

May 13, 2026cs.LG

Decoupled and Divergence-Conditioned Prompt for Multi-domain Dynamic Graph Foundation Models

Dynamic graphs are ubiquitous in real-world systems, and building generalizable dynamic Graph Foundation Models has become a frontier in graph learning. However, dynamic graphs from different domains pose fundamental challenges to unified modeling, as their semantic and temporal patterns are inherently inconsistent, making the multi-domain pre-training difficult. Consequently, the widely used "pretrain-then-finetune" paradigm often suffers from severe negative knowledge transfer. To the best of our knowledge, there exists no multi-domain dynamic GFM. In this work, we propose DyGFM, a Dynamic Graph Foundation Model over multiple domains based on decoupled and divergence-conditioned prompting. To disentangle transferable semantics from the domain-specific dynamics, we introduce a dual-branch pre-training strategy with semantic-temporal decoupling. To alleviate negative transfer during domain adaptation, we further develop a cross-domain routing mechanism with divergence-aware expert selection. To enable efficient downstream fine-tuning, we design a divergence-conditioned prompt generator that injects lightweight, learnable graph prompts tailored to semantic and temporal traits. Extensive experiments on continuous dynamic graph benchmarks demonstrate that DyGFM consistently outperforms 12 state-of-the-art baselines on both node classification and link prediction tasks, achieving superior effectiveness and efficiency.

Haonan Yuan, Qingyun Sun, Junhua Shi +3

Domain-Adaptive Pretraining Prompt Tuning Cross-Domain Transfer Learning Dynamic Graph Learning Graph Foundation Models

May 11, 2026cs.LG

Learning Graph Foundation Models on Riemannian Graph-of-Graphs

Graph foundation models (GFMs), pretrained on massive graph data, have transformed graph machine learning by supporting general-purpose reasoning across diverse graph tasks and domains. Existing GFMs pretrained with fixed-hop subgraph sampling impose a fixed receptive field, causing scale mismatch on diverse tasks, which often require heterogeneous and unknown structural contexts beyond a fixed sampling scale. We propose R-GFM, a Riemannian Graph-of-Graphs (GoG) based foundation model, that treats structural scale as a first-class citizen in modeling. R-GFM constructs a multi-scale GoG over-sampled subgraphs at different hop distances and learns geometry-adaptive representations from Riemannian manifolds. Theoretical analysis shows that R-GFM reduces structural domain generalization error compared to fixed-scale GFMs. Experiments on various datasets demonstrate that R-GFM achieves state-of-the-art performance, with up to a 49% relative improvement on downstream tasks. Our code is available at https://github.com/USTC-DataDarknessLab/R-GFM.

Haokun Liu, Zezhong Ding, Xike Xie

School of Biomedical Engineering, University of Science and Technology of China (USTC), Suzhou, Jiangsu, China · Data Darkness Lab, Suzhou Institute for Advanced Research, USTC, Suzhou, Jiangsu, China · School of Artificial Intelligence and Data Science, USTC, Hefei, Anhui, China

Graph Representation Learning Domain Generalization Geometric Representation Learning Graph Foundation Models

May 9, 2026cs.LG

Structure-Centric Graph Foundation Model via Geometric Bases

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov-Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Xiaodong He, Haolan He, Ruiyi Fang +2

University of Electronic Science and Technology of China, Chengdu, Sichuan Province, China · Western University

Geometric Representation Learning Graph Foundation Models

May 7, 2026cs.AI

Graphlets as Building Blocks for Structural Vocabulary in Knowledge Graph Foundation Models

Foundation models excel at language, where sentences become tokens, and vision, where images become pixels, because both reduce to discrete symbols on a shared, fixed grid. Knowledge Graphs share the discreteness, but not the geometry. Their entities and relations are discrete symbols, yet their arrangement is relational and lacks a common, fixed grid. Knowledge Graphs (KGs) share the discreteness, but not the geometry. They form irregular, non-Euclidean topologies whose local neighborhoods differ from graph to graph. Therefore, Knowledge Graph Foundation Models (KGFMs) rely on identifying structural invariances to produce transferable representations. Without a universal token set, KGFMs are limited in their ability to transfer representations across unseen KGs. We close this gap by treating graphlets, small connected graphs, as structural tokens that recur in heterogeneous KGs. In this paper, We introduce a model-agnostic framework based on a vocabulary of graphlets that mines a KG between relations via pattern matching. In particular, we considered closed and open 2- and 3-path, and star graphlets, to obtain robust invariances. The framework is evaluated on 51 KGs from a wide range of domains, for zero-shot inductive and transductive link prediction. Experiments show that adding simple graphlets to the vocabulary yields models that outperform prior KGFMs.

Kossi Amouzouvi, Robert Wardenga, Jens Lehmann +1

ScaDS.AI Dresden/Leipzig, Technische Universität Dresden, Dresden, Germany · alphaspeech - c/o alpha NT GmbH, Dresden, Germany · Amazon, Technische Universität Dresden, Dresden, Germany +1

Graph Representation Learning Graph Foundation Models KG Completion

May 6, 2026cs.LG

Bridging Input Feature Spaces Towards Graph Foundation Models

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.

Moshe Eliasof, Krishna Sri Ipsit Mantri, Beatrice Bevilacqua +2

University of Cambridge · Ben-Gurion University of the Negev · Purdue University

Graph Representation Learning Transfer Learning Graph Foundation Models Invariant Representation Learning

May 5, 2026cs.CL

Revisiting Graph-Tokenizing Large Language Models: A Systematic Evaluation of Graph Token Understanding

The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph tasks. As a widely recognized paradigm, Graph-Tokenizing LLMs (GTokenLLMs) compress complex graph data into graph tokens and treat them as prefix tokens for querying LLMs, leading many to believe that LLMs can understand graphs more effectively and efficiently. In this paper, we challenge this belief: \textit{Do GTokenLLMs fully understand graph tokens in the natural-language embedding space?} Motivated by this question, we formalize a unified framework for GTokenLLMs and propose an evaluation pipeline, \textbf{GTEval}, to assess graph-token understanding via instruction transformations at the format and content levels. We conduct extensive experiments on 6 representative GTokenLLMs with GTEval. The primary findings are as follows: (1) Existing GTokenLLMs do not fully understand graph tokens. They exhibit over-sensitivity or over-insensitivity to instruction changes, and rely heavily on text for reasoning; (2) Although graph tokens preserve task-relevant graph information and receive attention across LLM layers, their utilization varies across models and instruction variants; (3) Additional instruction tuning can improve performance on the original and seen instructions, but it does not fully address the challenge of graph-token understanding, calling for further improvement.

Zhongjian Zhang, Yue Yu, Mengmei Zhang +3

Beijing University of Posts and Telecommunications · China Telecom Bestpay · Beihang University

LLM Evaluation LLM Reasoning with Graphs Graph Foundation Models LLMs for Graph Learning

May 1, 2026cs.SI

Empowering Heterogeneous Graph Foundation Models via Decoupled Relation Alignment

While Graph Foundation Models (GFMs) have achieved remarkable success in homogeneous graphs, extending them to multi-domain heterogeneous graphs (MDHGs) remains a formidable challenge due to cross-type feature shifts and intra-domain relation gaps. Existing global feature alignment methods (PCA or SVD) enforce a shared feature space blindly, which distorts type-specific semantics and disrupts original topologies, inevitably leading to "Type Collapse" and "Relation Confusion". To address these fundamental limitations, we propose Decoupled relation Subspace Alignment (DRSA), a novel, plug-and-play relation-driven alignment framework. DRSA fundamentally shifts the paradigm by decoupling feature semantics from relation structures. Specifically, it introduces a dual-relation subspace projection mechanism to coordinate cross-type interactions within a shared low-rank relation subspace explicitly. Furthermore, a feature-structure decoupled representation is designed to decompose aligned features into a semantic projection component and a structural residual term, adaptively absorbing intra-domain variations. Optimized via a stable alternating minimization strategy based on Block Coordinate Descent, DRSA constructs a well-calibrated, structure-aware latent space. Extensive experiments on multiple real-world benchmark datasets demonstrate that DRSA can be seamlessly integrated as a universal preprocessing module, significantly and consistently enhancing the cross-domain and few-shot knowledge transfer capabilities of state-of-the-art GFMs. The code is available at: https://github.com/zhengziyu77/DSRA.

Ziyu Zheng, Yaming Yang, Zhe Wang +2

School of Computer Science and Technology, Xidian University, Xi’an, China 710071

Heterogeneous GNNs Cross-Domain Transfer Learning Graph Foundation Models

Apr 23, 2026cs.LG

Mochi: Aligning Pre-training and Inference for Efficient Graph Foundation Models via Meta-Learning

We propose Mochi, a Graph Foundation Model that addresses task unification and training efficiency by adopting a meta-learning based training framework. Prior models pre-train with reconstruction-based objectives such as link prediction, and assume that the resulting representations can be aligned with downstream tasks through a separate unification step such as class prototypes. We demonstrate through synthetic and real-world experiments that this procedure, while simple and intuitive, has limitations that directly affect downstream task performance. To address these limitations, Mochi pre-trains on few-shot episodes that mirror the downstream evaluation protocol, aligning the training objective with inference rather than relying on a post-hoc unification step. We show that Mochi, along with its more powerful variant Mochi++, achieves competitive or superior performance compared to existing Graph Foundation Models across 25 real-world graph datasets spanning node classification, link prediction, and graph classification, while requiring 8

\sim

27 times less training time than the strongest baseline.

João Mattos, Arlei Silva

Computer Science Department · Ken Kennedy Institute

Graph Representation Learning Meta-Learning Graph Foundation Models