Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding

TL;DR

This paper introduces a novel sheaf-theoretic framework for knowledge graph embedding, enabling more flexible reasoning and incorporation of prior constraints by viewing embeddings as sections of a knowledge sheaf.

Contribution

It presents a new topological and categorical approach to knowledge graph embedding using cellular sheaves, broadening the theoretical foundation and practical capabilities.

Findings

Framework generalizes existing embedding models

Allows reasoning with composite relations without retraining

Demonstrates benefits through implementation and experiments

Abstract

Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of \textit{cellular sheaves}: a knowledge graph embedding can be described as an approximate global section of an appropriate \textit{knowledge sheaf} over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.