Data Interpolations in Deep Generative Models under Non-Simply-Connected Manifold Topology

TL;DR

This paper introduces a density regularizer to improve data interpolation in deep generative models by addressing topological differences, such as holes and disconnected regions, in the learned data-manifold.

Contribution

A novel density regularizer that enables better interpolation across non-simply-connected manifolds in deep generative models.

Findings

Improved interpolation results on real-world image datasets.

The regularizer effectively circumvents holes in the data-manifold.

Enhanced handling of topological complexities in generative modeling.

Abstract

Exploiting the deep generative model's remarkable ability of learning the data-manifold structure, some recent researches proposed a geometric data interpolation method based on the geodesic curves on the learned data-manifold. However, this interpolation method often gives poor results due to a topological difference between the model and the dataset. The model defines a family of simply-connected manifolds, whereas the dataset generally contains disconnected regions or holes that make them non-simply-connected. To compensate this difference, we propose a novel density regularizer that make the interpolation path circumvent the holes denoted by low probability density. We confirm that our method gives consistently better interpolation results from the experiments with real-world image datasets.