Hyperbolic embeddings have recently gained attention in machine learning due
to their ability to represent hierarchical data more accurately and succinctly
than their Euclidean analogues. However, multi-relational knowledge graphs
often exhibit multiple simultaneous hierarchies, which current hyperbolic
models do not capture. To address this, we propose a model that embeds
multi-relational graph data in the Poincar\'e ball model of hyperbolic space.
Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific
parameters to transform entity embeddings by M\"obius matrix-vector
multiplication and M\"obius addition. Experiments on the hierarchical WN18RR
knowledge graph show that our Poincar\'e embeddings outperform their Euclidean
counterpart and existing embedding methods on the link prediction task,
particularly at lower dimensionality.

本研究提出了一种称为 MuRP 的多关系泊松球模型，用于在 Poincaré 空间中嵌入多关系图数据，并学习关系特定参数以通过 Möbius 矩阵 - 向量乘法和 Möbius 相加来转换嵌入，实验表明 Poincare 嵌入在链接预测任务中比欧几里得模型和现有嵌入方法的效果更好，特别是在低维度的情况下。

多关系 Poincaré 图嵌入

Multi-relational Poincaré Graph Embeddings

Latent factor models are increasingly popular for modeling multi-relational
knowledge graphs. By their vectorial nature, it is not only hard to interpret
why this class of models works so well, but also to understand where they fail
and how they might be improved. We conduct an experimental survey of
state-of-the-art models, not towards a purely comparative end, but as a means
to get insight about their inductive abilities. To assess the strengths and
weaknesses of each model, we create simple tasks that exhibit first, atomic
properties of binary relations, and then, common inter-relational inference
through synthetic genealogies. Based on these experimental results, we propose
new research directions to improve on existing models.

本文研究了潜在的因素模型在多关系知识图谱建模中的应用，通过实验测试和分析这些模型的归纳能力和优缺点，并提出了未来改进的方向。