AI中文摘要
知识图谱上的多跳逻辑推理需要将逻辑语义忠实地映射到潜在空间。当前的几何嵌入方法通过将实体映射到几何区域、逻辑操作映射到潜在变换，在此任务上表现出有效性。虽然几何嵌入可以为查询回答提供直接的可解释性框架，但当前方法仅利用了实体的几何构造，未能将逻辑操作映射为纯几何变换，而是使用神经组件来学习这些操作。另一方面，纯神经方法优于几何方法，但在潜在空间中缺乏可解释性。我们提出了GeometrE，一种用于多跳推理的几何嵌入方法，它将每个逻辑操作映射为潜在空间中的纯几何操作。此外，我们引入了一个传递损失函数，并表明与现有方法不同，它可以保留对所有a,b,c的逻辑规则：r(a,b)和r(b,c) -> r(a,c)。我们的实验表明，GeometrE优于当前最先进的几何方法，并在标准基准数据集上与现有的神经方法保持竞争力。
英文摘要
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.
