# To Learn is to Wander: Learning Across Graphs and Tasks with Random Walks

arXiv: https://arxiv.org/abs/2610.06694 · HTML: https://mlsanity.com/paper/2610.06694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 76 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [LimiX: Unleashing Structured-Data Modeling Capability for Generalist Intelligence](https://mlsanity.com/paper/2509.03505/) (2025)
- [Turning Tabular Foundation Models into Graph Foundation Models](https://mlsanity.com/paper/2508.20906/) (2025)
- [A Multi-Task Perspective for Link Prediction with New Relation Types and Nodes](https://mlsanity.com/paper/2307.06046/) (2023)
- [TabPFN-3: Technical Report](https://mlsanity.com/paper/2605.13986/) (2026)
- [Bringing Graphs to the Table: Zero-shot Node Classification via Tabular Foundation Models](https://mlsanity.com/paper/2509.07143/) (2025)
- [Universal Link Predictor By In-Context Learning on Graphs](https://mlsanity.com/paper/2402.07738/) (2024)
- [TFMLinker: Universal Link Predictor by Graph In-Context Learning with Tabular Foundation Models](https://mlsanity.com/paper/2602.08592/) (2026)

## Abstract (arXiv)

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.