论文标题
双曲线表示：一种最佳基于运输的方法
Aligning Hyperbolic Representations: an Optimal Transport-based approach
论文作者
论文摘要
双曲空空间更适合表示具有潜在分层关系的数据，例如树状数据。但是，通常有必要通过对齐方式合并不同但相关的表示形式。这种对齐是一类重要的机器学习问题类别，其应用程序是本体匹配和跨语言对齐。基于最佳传输（OT）的方法是解决对齐问题的自然选择，因为它们旨在找到源数据集的转换以匹配目标数据集，但要受到某些分布约束。这项工作提出了一种基于OT嵌入在双曲线空间模型上的新方法。我们的方法依赖于Möbius陀螺仪空间上的陀螺疗图。由于这种形式主义，我们将基于OT的域适应其双曲线对应物的某些现有欧几里得方法扩展。从经验上讲，我们表明欧几里得和双曲线方法在检索的背景下都具有相似的性能。
Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully. This aligning is an important class of machine learning problems, with applications as ontology matching and cross-lingual alignment. Optimal transport (OT)-based approaches are a natural choice to tackle the alignment problem as they aim to find a transformation of the source dataset to match a target dataset, subject to some distribution constraints. This work proposes a novel approach based on OT of embeddings on the Poincaré model of hyperbolic spaces. Our method relies on the gyrobarycenter mapping on Möbius gyrovector spaces. As a result of this formalism, we derive extensions to some existing Euclidean methods of OT-based domain adaptation to their hyperbolic counterparts. Empirically, we show that both Euclidean and hyperbolic methods have similar performances in the context of retrieval.
