  Foundation models in language and vision have the ability to run inference on
any textual and visual inputs thanks to the transferable representations such
as a vocabulary of tokens in language. Knowledge graphs (KGs) have different
entity and relation vocabularies that generally do not overlap. The key
challenge of designing foundation models on KGs is to learn such transferable
representations that enable inference on any graph with arbitrary entity and
relation vocabularies. In this work, we make a step towards such foundation
models and present ULTRA, an approach for learning universal and transferable
graph representations. ULTRA builds relational representations as a function
conditioned on their interactions. Such a conditioning strategy allows a
pre-trained ULTRA model to inductively generalize to any unseen KG with any
relation vocabulary and to be fine-tuned on any graph. Conducting link
prediction experiments on 57 different KGs, we find that the zero-shot
inductive inference performance of a single pre-trained ULTRA model on unseen
graphs of various sizes is often on par or better than strong baselines trained
on specific graphs. Fine-tuning further boosts the performance.
