Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors

One of the most challenging problems in graph machine learning is generalizing across graphs with diverse properties. Graph neural networks (GNNs) face a fundamental limitation: they require separate training for each new graph, preventing universal generalization across diverse graph datasets. A critical challenge facing GNNs lies in their reliance on labeled training data for each individual graph, a requirement that hinders the capacity for universal node classification due to the heterogeneity inherent in graphs --- differences in homophily levels, community structures, and feature distributions across datasets. Inspired by the success of large language models (LLMs) that achieve in-context learning through massive-scale pre-training on diverse datasets, we introduce NodePFN. This universal node classification method generalizes to arbitrary graphs without graph-specific training. NodePFN learns posterior predictive distributions (PPDs) by training only on thousands of synthetic graphs generated from carefully designed priors. Our synthetic graph generation covers real-world graphs through the use of random networks with controllable homophily levels and structural causal models for complex feature-label relationships. We develop a dual-branch architecture combining context-query attention mechanisms with local message passing to enable graph-aware in-context learning. Extensive evaluation on 23 benchmarks demonstrates that a single pre-trained NodePFN achieves 71.27\% average accuracy. These results validate that universal graph learning patterns can be effectively learned from synthetic priors, establishing a new paradigm for generalization in node classification.