Structure-Centric Graph Foundation Model via Geometric Bases

Graph foundation models (GFMs) aim to learn transferable representations across severely heterogeneous graph domains. However, severe domain shifts in topology, graph scale, and feature semantics impede the construction of a unified, domain-agnostic representation space. To address this, we propose SCGFM-ART, a structure-centric GFM framework that aligns arbitrary graphs onto a shared relational atlas via Amortized Relational Transport (ART). The relational atlas serves as a universal coordinate system defined by a finite set of relational landmarks (bases), while ART directly predicts reusable, end-to-end graph-to-base transport plans, bypassing costly runtime Gromov-Wasserstein optimizations. Under this formulation, SCGFM-ART decomposes a graph into a unified representation: globally via its relational response coordinates relative to the atlas, and locally via its node-to-role structural correspondences. These correspondences project disparate node attributes into a canonical role space, resolving structural and semantic heterogeneity within a singular alignment interface. Rigorously modeling graphs and atlas bases as finite measured relational spaces, we establish coordinate fidelity bounds, prove stability under predicted transport plans, and derive an amortized coverage bound that guarantees our learning objective tightly surrogates ideal relational coverage. Benchmarked across 14 cross-domain graph- and node-level classification tasks, SCGFM-ART achieves state-of-the-art transferability, securing superior average ranks of 2.29 and 1.14, respectively. Topological perturbation analyses demonstrate that node-role transport retains fine-grained structural nuances beyond global coordinates. On real-world benchmarks, the amortized formulation yields 44.2 to 85.1 times faster frozen target-domain inference by avoiding iterative alignment at test time.

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 emerged as a promising paradigm for learning transferable representations across diverse graph domains. Recent advancements in GFMs have been largely dominated by two paradigms: Graph Neural Network and Large Language Model (LLM) based methods. However, these methods often face a fundamental dilemma between training with limited data and a heavy reliance on textual attributes. Tabular foundation models (TFMs) offer a potential alternative, as node features and representations can be naturally organized in a tabular form. However, how to enable TFMs to effectively capture structural information of graphs remains largely unexplored. The key challenge is to learn a graph-to-table alignment mechanism that enables graph structural understanding for TFMs. To address this, we propose GTAlign, a surprisingly simple yet effective Graph-to-Table Alignment framework for text-free Graph Foundation Model. Specifically, we first pretrain a graph encoder that maps diverse graphs into a unified latent space to capture domain-agnostic graph representations. To further bridge the gap between graph topology and the tabular representation space, we propose community-guided continual pre-training, where pseudo-labels derived from graph community are used to construct few-shot prediction episodes. Lastly, we adapt the graph encoder for an unseen target domain and perform in-context inference. Extensive experiments on five benchmark datasets demonstrate that GTAlign significantly outperforms state-of-the-art baselines on both node and graph classification, offering a simple, effective, and text-free GFM model. Code will be released upon acceptance.