Feature Propagation on Knowledge Graphs using Cellular Sheaves
This addresses the challenge of handling new entities in knowledge graphs for tasks like relation prediction, offering a novel algebraic approach with practical improvements.
The paper tackles the problem of inductive knowledge graph reasoning by using cellular sheaves to propagate embeddings from known subgraphs to new entities, achieving competitive or superior performance on large-scale benchmarks compared to specialized models.
Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relations) that preserve task-relevant structure encoded within the underlying combinatorial object. Such knowledge graph embeddings can be modeled as an approximate global section of a cellular sheaf, an algebraic structure over the graph. Using the diffusion dynamics encoded by the corresponding sheaf Laplacian, we optimally propagate known embeddings of a subgraph to inductively represent new entities introduced into the knowledge graph at inference time. We implement this algorithm via an efficient iterative scheme and show that on a number of large-scale knowledge graph embedding benchmarks, our method is competitive with -- and in some scenarios outperforms -- more complex models derived explicitly for inductive knowledge graph reasoning tasks.