Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs

TL;DR

BetaE introduces a probabilistic embedding framework using Beta distributions to perform multi-hop logical reasoning over knowledge graphs, supporting all FOL operators including negation and modeling uncertainty.

Contribution

It is the first method capable of handling complete first-order logic operations in KG reasoning, improving over existing methods that lack negation support.

Findings

BetaE outperforms state-of-the-art methods by up to 25.4% in reasoning accuracy.

It effectively models uncertainty in logical reasoning over KGs.

Supports arbitrary FOL queries including negation, conjunction, and disjunction.

Abstract

One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty. Here, we present BetaE, a probabilistic embedding framework for answering arbitrary FOL queries over KGs. BetaE is the first method that can handle a complete set of first-order logical operations: conjunction ($\wedge$), disjunction ($\vee$), and negation ($\neg$). A key insight of BetaE is to use probabilistic distributions with bounded support, specifically the Beta distribution, and embed queries/entities as distributions, which as a consequence allows us to also faithfully model uncertainty. Logical operations are performed in the embedding space by neural operators over the probabilistic embeddings. We demonstrate the performance of BetaE on answering arbitrary FOL queries on three large, incomplete KGs. While being more general, BetaE also increases relative performance by up to 25.4% over the current state-of-the-art KG reasoning methods that can only handle conjunctive queries without negation.