The Universal Classifier for Graph Learning

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.

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.

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.