Training Graph Foundation Models on The Web Graph

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.

Graph foundation models aim to transfer across graphs, feature spaces, relational schemas, and prediction tasks, yet existing approaches typically generalize only within particular graph modalities or tasks. We propose Wander, a graph foundation model designed to operate across these settings within a single pretrained checkpoint. Following the prior-predictive perspective, we formulate graph learning as completion of a partially observed graph. We realize this task-general view through a common interface based on random walks, allowing the same model to operate across homogeneous and multi-relational graphs with varying features, labels, and relational schemas. Wander can increase its structural context at inference time without changing its learned parameters and, under suitable assumptions, universally approximates the corresponding Bayes-optimal predictor on bounded connected graphs. Empirically, a single pretrained checkpoint achieves state-of-the-art or highly competitive results across node classification, homogeneous link prediction, and knowledge-graph link prediction. Moreover, joint pretraining across graph modalities and tasks preserves performance in specialized settings while enabling positive transfer and the composition of separately learned capabilities at inference time.

Designing foundation models for graphs is challenging due to the irregular structure of graphs and the different sizes and characteristics of embeddings. Chimaera integrates mixture-of-experts with graph foundation models (GFM). It integrates different GFM architectures, such as graph prompts and linear GNN models. Large language models are used to generate embeddings, and experts can be trained and combined following different strategies, GFMs, embeddings, etc. Furthermore, Chimaera extends existing linear GNNs to support link-level and graph-level tasks in addition to node-level tasks. Empirical analyses are performed on same-task and cross-task experiments with node, link, and graph classification tasks using six benchmark text-attributed graph datasets. The experiments demonstrate the effectiveness of Chimaera and its capabilities for transfer across tasks and datasets. Further insights include the need to use both large and small language models to generate embeddings for the experts, a strong cross-task transferability of simple but effective linear GNNs, and using few samples only to provide strong results.