Decoder ensembling for learned latent geometries
This work addresses a fundamental issue in latent space geometry for researchers in machine learning, offering a principled method to improve analysis in generative models.
The paper tackled the problem of topological mismatch between Euclidean latent spaces and complex data manifolds in deep generative models by proposing decoder ensembling to capture model uncertainty and compute geodesics on the expected manifold, finding this approach simple and reliable.
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.