Feature Propagation on Knowledge Graphs using Cellular Sheaves

TL;DR

This paper introduces a novel method for propagating knowledge graph embeddings using cellular sheaves and their Laplacian diffusion dynamics, enabling inductive reasoning and outperforming some existing models on large-scale benchmarks.

Contribution

It models knowledge graph embeddings as sections of cellular sheaves and uses sheaf Laplacian diffusion for inductive embedding propagation, a novel approach in the field.

Findings

Method is competitive with existing models on large-scale benchmarks.

Outperforms some complex models in inductive reasoning tasks.

Efficient iterative implementation enables practical application.

Abstract

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.