Decoder ensembling for learned latent geometries

TL;DR

This paper introduces a decoder ensembling method to better capture the latent space geometry of deep generative models, enabling more accurate geodesic computations and addressing topological mismatches.

Contribution

It proposes using ensembles of decoders to model uncertainty and compute geodesics on the expected manifold, improving latent space analysis.

Findings

Ensembles effectively capture model uncertainty in latent spaces.

Geodesic computations on the ensemble-based manifold are reliable.

Method advances the practical use of latent geometries in deep generative models.

Abstract

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric, allowing for a standard differential geometric analysis of the latent space. Unfortunately, data manifolds are generally compact and easily disconnected or filled with holes, suggesting a topological mismatch to the Euclidean latent space. The most established solution to this mismatch is to let uncertainty be a proxy for topology, but in neural network models, this is often realized through crude heuristics that lack principle and generally do not scale to high-dimensional representations. We propose using ensembles of decoders to capture model uncertainty and show how to easily compute geodesics on the associated expected manifold. Empirically, we find this simple and reliable, thereby coming one step closer to easy-to-use latent geometries.