Fully Geometric Multi-Hop Reasoning on Knowledge Graphs with Transitive Relations
This work addresses interpretability and performance in knowledge graph reasoning for AI applications, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles the problem of multi-hop reasoning on knowledge graphs by introducing GeometrE, a fully geometric embedding method that maps logical operations to geometric transformations without neural components, and it outperforms state-of-the-art methods on standard benchmarks.
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.