# Latent Space Cartography: Generalised Metric-Inspired Measures and Measure-Based Transformations for Generative Models

arXiv: https://arxiv.org/abs/1902.02113 · HTML: https://mlsanity.com/paper/1902.02113/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Reliable Measures of Spread in High Dimensional Latent Spaces](https://mlsanity.com/paper/2212.08172/) (2022)
- [Explainable AI for Multivariate Time Series Pattern Exploration: Latent Space Visual Analytics with Temporal Fusion Transformer and Variational Autoencoders in Power Grid Event Diagnosis](https://mlsanity.com/paper/2412.16098/) (2024)
- [LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecture](https://mlsanity.com/paper/2603.07246/) (2026)

## Abstract (arXiv)

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.