Poincar\'e Wasserstein Autoencoder

TL;DR

This paper introduces a Poincaré Wasserstein Autoencoder that models latent space in hyperbolic geometry, leveraging its hierarchical structure to improve representation learning, with applications in visual data and graph link prediction.

Contribution

It reformulates Wasserstein autoencoders on hyperbolic space, enabling structured latent representations that capture hierarchical relationships.

Findings

Competitive results on graph link prediction

Effective modeling of hierarchical data in visual tasks

Demonstrates advantages of hyperbolic latent space

Abstract

This work presents a reformulation of the recently proposed Wasserstein autoencoder framework on a non-Euclidean manifold, the Poincar\'e ball model of the hyperbolic space. By assuming the latent space to be hyperbolic, we can use its intrinsic hierarchy to impose structure on the learned latent space representations. We demonstrate the model in the visual domain to analyze some of its properties and show competitive results on a graph link prediction task.