Aligning Hyperbolic Representations: an Optimal Transport-based approach

Understand

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.