GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs

TL;DR

GammaE introduces a probabilistic gamma embedding model that effectively handles negation and union operators for logical reasoning on knowledge graphs, significantly improving performance over existing methods.

Contribution

The paper presents GammaE, a novel gamma distribution-based embedding model that models negation and union operators more accurately for logical queries on knowledge graphs.

Findings

GammaE outperforms state-of-the-art models on benchmark datasets.

GammaE effectively models negation with clear boundaries, reducing ambiguity.

GammaE's union operator is closed, enabling complex query compositions.

Abstract

Embedding knowledge graphs (KGs) for multi-hop logical reasoning is a challenging problem due to massive and complicated structures in many KGs. Recently, many promising works projected entities and queries into a geometric space to efficiently find answers. However, it remains challenging to model the negation and union operator. The negation operator has no strict boundaries, which generates overlapped embeddings and leads to obtaining ambiguous answers. An additional limitation is that the union operator is non-closure, which undermines the model to handle a series of union operators. To address these problems, we propose a novel probabilistic embedding model, namely Gamma Embeddings (GammaE), for encoding entities and queries to answer different types of FOL queries on KGs. We utilize the linear property and strong boundary support of the Gamma distribution to capture more features of entities and queries, which dramatically reduces model uncertainty. Furthermore, GammaE implements the Gamma mixture method to design the closed union operator. The performance of GammaE is validated on three large logical query datasets. Experimental results show that GammaE significantly outperforms state-of-the-art models on public benchmarks.