Learning a Prior-Data Fitted Network for Graph Foundation Models via Structural Causal Model Priors

Graph foundation models face several fundamental challenges including transferability across diverse domains and data scarcity, which calls into question the very feasibility of creating such models. However, despite similar challenges, the tabular domain has recently witnessed the emergence of the first successful foundation models such as TabPFN. These models are based on the prior-data fitted networks (PFN) framework, in which models are pretrained on carefully designed synthetic datasets to make predictions in an in-context learning setting. Recently, G2T-FM, a framework that converts graph node-level tasks into tabular tasks, has made the first step towards adopting PFNs for graphs, yet it is limited to hand-crafted features and was never pretrained on graph data. In this work, we make the next step by proposing GraphPFN, a PFN-based model designed and pretrained specifically for graph node-level tasks. Following the PFN framework, we first design a prior distribution of synthetic attributed graphs by using a novel combination of multi-level stochastic block models and a preferential attachment process for structure generation and graph-aware structured causal models for attribute generation. Then, we augment the tabular foundation model LimiX with attention-based graph neighborhood aggregation layers and train it on millions of synthetic graphs sampled from our prior. On diverse real-world graph datasets with node-level tasks, GraphPFN achieves state-of-the-art results in both in-context learning and finetuning regimes, outperforming G2T-FM, prior GFMs, and task-specific GNNs trained from scratch. More broadly, GraphPFN shows the potential of PFN-based models for building graph foundation models.

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.

Prior-data fitted networks (PFNs) show that pretraining on large populations of synthetic tasks can enable generalization to unseen datasets with little or no downstream fine-tuning. This paradigm is effective for transformer-based tabular and relational foundation models such as RDB-PFN, but remains largely unexplored for graph-based relational models built on message passing. We pretrain the graph-based relational foundation model Griffin on large collections of synthetic relational databases and ask whether curriculum learning, which benefits transformer-based relational learners, also improves message-passing representations. Rather than fine-tune on downstream tasks, we use the pretrained encoder as a general-purpose relational representation learner and pass its latent representations to a frozen in-context predictor (\ticl{}); no component is trained on the target task. On 16 real-world relational classification tasks, evaluated over five seeds against raw-feature and untrained-encoder baselines, a purely synthetic curriculum that begins with schema-guided data and continues with schema-agnostic data gives the strongest frozen in-context performance\rev{, outperforming real-data-only pretraining and every unordered single-stage mixture of the corpora; when appended after real-data pretraining, it yields the best encoders overall}. These results provide initial evidence that PFN-style synthetic pretraining transfers to graph-based relational foundation models.