Latent Space Cartography: Generalised Metric-Inspired Measures and Measure-Based Transformations for Generative Models
Abstract
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous results on Riemannian metrics. We show how a class of heuristic measures gives more flexibility in finding meaningful, problem-specific distances, and how it can be applied to diverse generator types such as autoregressive generators commonly used in e.g. language and other sequence modeling. We further demonstrate how a diffusion-inspired transformation previously studied in cartography can be used to smooth out latent spaces, stretching them according to a chosen measure. In addition to providing more meaningful distances directly in latent space, this also provides a unique tool for novel kinds of data visualizations. We believe that the proposed methods can be a valuable tool for studying the structure of latent spaces and learned data distributions of generative models.
Cite
@article{arxiv.1902.02113,
title = {Latent Space Cartography: Generalised Metric-Inspired Measures and Measure-Based Transformations for Generative Models},
author = {Max F. Frenzel and Bogdan Teleaga and Asahi Ushio},
journal= {arXiv preprint arXiv:1902.02113},
year = {2019}
}