Data Interpolations in Deep Generative Models under Non-Simply-Connected Manifold Topology
This addresses a specific issue in generative modeling for image data, offering an incremental improvement to interpolation methods.
The paper tackles the problem of poor geometric data interpolation in deep generative models caused by topological mismatches between simply-connected model manifolds and non-simply-connected datasets, and proposes a density regularizer that improves interpolation results, as confirmed by experiments on real-world image datasets.
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.