Reasoning with knowledge graphs (KGs) has primarily focused on triple-shaped
facts. Recent advancements have been explored to enhance the semantics of these
facts by incorporating more potent representations, such as hyper-relational
facts. However, these approaches are limited to \emph{atomic facts}, which
describe a single piece of information. This paper extends beyond \emph{atomic
facts} and delves into \emph{nested facts}, represented by quoted triples where
subjects and objects are triples themselves (e.g., ((\emph{BarackObama},
\emph{holds\_position}, \emph{President}), \emph{succeed\_by},
(\emph{DonaldTrump}, \emph{holds\_position}, \emph{President}))). These nested
facts enable the expression of complex semantics like \emph{situations} over
time and \emph{logical patterns} over entities and relations. In response, we
introduce NestE, a novel KG embedding approach that captures the semantics of
both atomic and nested factual knowledge. NestE represents each atomic fact as
a $1\times3$ matrix, and each nested relation is modeled as a $3\times3$ matrix
that rotates the $1\times3$ atomic fact matrix through matrix multiplication.
Each element of the matrix is represented as a complex number in the
generalized 4D hypercomplex space, including (spherical) quaternions,
hyperbolic quaternions, and split-quaternions. Through thorough analysis, we
demonstrate the embedding's efficacy in capturing diverse logical patterns over
nested facts, surpassing the confines of first-order logic-like expressions.
Our experimental results showcase NestE's significant performance gains over
current baselines in triple prediction and conditional link prediction. The
code and pre-trained models are open available at
this https URL

本文介绍了一个名为 NestE 的新型知识图嵌入方法，通过将原子事实表示成一个 1x3 矩阵，将嵌套关系表示成一个 3x3 矩阵，通过矩阵乘法旋转原子事实矩阵，利用广义四维超复数空间（如球面四元数、双曲四元数和分裂四元数）来表示矩阵的每个元素，从而能够捕捉嵌套事实中多样的逻辑模式，超越了一阶逻辑表达式的限制。实验结果表明，NestE 在三元组预测和条件链接预测方面显著优于当前基线模型。

NestE：建模知识图谱推理的嵌套关系结构

NestE: Modeling Nested Relational Structures for Knowledge Graph  Reasoning

Knowledge graph (KG) embeddings learn low-dimensional representations of
entities and relations to predict missing facts. KGs often exhibit hierarchical
and logical patterns which must be preserved in the embedding space. For
hierarchical data, hyperbolic embedding methods have shown promise for
high-fidelity and parsimonious representations. However, existing hyperbolic
embedding methods do not account for the rich logical patterns in KGs. In this
work, we introduce a class of hyperbolic KG embedding models that
simultaneously capture hierarchical and logical patterns. Our approach combines
hyperbolic reflections and rotations with attention to model complex relational
patterns. Experimental results on standard KG benchmarks show that our method
improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in
mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that
different geometric transformations capture different types of relations while
attention-based transformations generalize to multiple relations. In high
dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR
and 57.7% on YAGO3-10.

本文介绍了一种超几何知识图嵌入方法，可以同时捕捉层次结构和逻辑模式，并在现有方法的基础上提高了平均倒数排名（MRR）达 6.1%。