Hence, each atomic term of the sum can be seen as a messagevectorbetween v andv'sneighbouringnode. In the paper, we chose DistMult and GD because of their mathematical simplicity,leading toeasier-to-read formulas. For example, here we offer a specific derivation for ComplEx[39]. For scalability w.r.t. the number of triplets/edges in the graph, we denote the entity set asE, the relation setasR,and the triplets asT. For inductive knowledge graph completion, we test the model on the new graph, where the relation vocabulary is shared with the training graph, while the entities are novel.

Factorisation-based Models (FMs), such as DistMult, have enjoyed enduring success for Knowledge Graph Completion (KGC) tasks, often outperforming Graph Neural Networks (GNNs). However, unlike GNNs, FMs struggle to incorporate node features and generalise to unseen nodes in inductive settings. Our work bridges the gap between FMs and GNNs by proposing ReFactor GNNs. This new architecture draws upon both modelling paradigms, which previously were largely thought of as disjoint. Concretely, using a message-passing formalism, we show how FMs can be cast as GNNs by reformulating the gradient descent procedure as message-passing operations, which forms the basis of our ReFactor GNNs. Across a multitude of well-established KGC benchmarks, our ReFactor GNNs achieve comparable transductive performance to FMs, and state-of-the-art inductive performance while using an order of magnitude fewer parameters.