Embedding Logical Queries on Knowledge Graphs

TL;DR

This paper introduces a novel embedding framework for knowledge graphs that efficiently answers complex logical queries involving multiple entities and relations, surpassing traditional simple edge prediction methods.

Contribution

The authors propose a geometric embedding approach that models logical operators as learned transformations, enabling scalable reasoning over conjunctive queries in large knowledge graphs.

Findings

Achieves linear time complexity in the number of query variables.

Successfully predicts complex logical relationships in large real-world datasets.

Demonstrates applicability to drug-gene-disease and social interaction networks.

Abstract

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that {\em might} interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.