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

[Submitted on 18 May 2025 (v1), last revised 17 Jun 2026 (this version, v2)]

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Abstract:Multi-hop logical reasoning on knowledge graphs requires faithfully mapping the logical semantics to latent space. Current geometric embedding methods show to be useful on this task by mapping entities to geometric regions and logical operations to latent transformations. While a geometric embedding can provide a direct interpretability framework for query answering, current methods have only leveraged the geometric construction of entities, failing to map logical operations to pure geometric transformations and, instead, using neural components to learn these operations. On the other hand, purely neural-based methods outperform geometric methods, but they lack interpretability in the latent space. We introduce GeometrE, a geometric embedding method for multi-hop reasoning, that maps every logical operation to a purely geometric operation in the latent space. Additionally, we introduce a transitive loss function and show that, unlike existing methods, it can preserve the logical rule for all a,b,c: r(a,b) and r(b,c) -> r(a,c). Our experiments show that GeometrE outperforms current state-of-the-art geometric methods and remains competitive with existing neural-based methods on standard benchmark datasets.

Submission history

From: Fernando Zhapa-Camacho [view email]
[v1] Sun, 18 May 2025 11:17:50 UTC (460 KB)
[v2] Wed, 17 Jun 2026 10:57:56 UTC (1,539 KB)