Aligning Hyperbolic Representations: an Optimal Transport-based approach
This work tackles the problem of aligning hyperbolic representations, which is important for applications like ontology matching and cross-lingual alignment, but the empirical results show no clear advantage over existing Euclidean methods.
This paper addresses the problem of aligning different hyperbolic representations, which are suitable for hierarchical data. The authors propose a novel optimal transport-based approach using gyrobarycenter mapping on Möbius gyrovector spaces, extending existing Euclidean methods to hyperbolic counterparts. Empirically, the method achieves similar retrieval performance to Euclidean methods.
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.