Atlas Generative Models and Geodesic Interpolation

TL;DR

This paper introduces Atlas Generative Models with hybrid latent spaces to better capture complex data manifold topologies and extends geodesic interpolation techniques to this broader class, demonstrated through experiments.

Contribution

It defines the class of Atlas Generative Models, integrating discrete and continuous latent spaces, and extends geodesic interpolation methods to these models.

Findings

AGMs can represent manifolds with complex topologies.

Geodesic interpolation is effectively generalized to AGMs.

Experimental results confirm the approach's validity.

Abstract

Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit into this class. Due to the atlas interpretation, ideas from non-linear latent space analysis and statistics, e.g. geodesic interpolation, which has previously only been investigated for models with simply connected latent spaces, may be extended to the entire class of AGMs in a natural way. We exemplify this by generalizing an algorithm for graph based geodesic interpolation to the setting of AGMs, and verify its performance experimentally.