Metrics for Deep Generative Models

TL;DR

This paper introduces a Riemannian geometry-based distance measure for deep generative models, improving the understanding and visualization of their latent spaces and enabling applications like robot movement generalization.

Contribution

It proposes a novel Riemannian metric for latent spaces of VAEs and GANs, offering a more meaningful similarity measure and visualization tool compared to traditional Euclidean distances.

Findings

The method accurately captures true distances in synthetic datasets.

It enhances visualization and interpolation in latent spaces.

Applicable to robot movement and human motion data.

Abstract

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that the density induced by a dataset contains large regions of low density, the training criterions of VAEs and GANs will make the latent space densely covered. Consequently points that are separated by low-density regions in observation space will be pushed together in latent space, making stationary distances poor proxies for similarity. We transfer ideas from Riemannian geometry to this setting, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In addition, it can be applied for robot movement generalization using previously learned skills. The method is evaluated on a synthetic dataset with known ground truth; on a simulated robot arm dataset; on human motion capture data; and on a generative model of handwritten digits.