Fully Geometric Multi-Hop Reasoning on Knowledge Graphs with Transitive Relations

TL;DR

GeometrE is a novel geometric embedding approach for multi-hop reasoning on knowledge graphs that preserves logical rules and offers full interpretability without learning logical operations.

Contribution

We propose GeometrE, a geometric embedding method that directly maps logical operations to geometric transformations and introduces a transitive loss for rule preservation.

Findings

Outperforms state-of-the-art methods on benchmark datasets

Successfully preserves transitive logical rules

Provides full geometric interpretability

Abstract

Geometric embedding methods have shown to be useful for multi-hop reasoning on knowledge graphs by mapping entities and logical operations to geometric regions and geometric transformations, respectively. Geometric embeddings provide direct interpretability framework for queries. However, current methods have only leveraged the geometric construction of entities, failing to map logical operations to geometric transformations and, instead, using neural components to learn these operations. We introduce GeometrE, a geometric embedding method for multi-hop reasoning, which does not require learning the logical operations and enables full geometric interpretability. Additionally, unlike previous methods, we introduce a transitive loss function and show that it can preserve the logical rule $\forall a,b,c: r(a,b) \land r(b,c) \to r(a,c)$. Our experiments show that GeometrE outperforms current state-of-the-art methods on standard benchmark datasets.