# Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions

arXiv: https://arxiv.org/abs/2005.07852 · HTML: https://mlsanity.com/paper/2005.07852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2020.

## Built on by (most cited first, 2 of 2)

- [On Linear Interpolation in the Latent Space of Deep Generative Models](https://mlsanity.com/paper/2105.03663/) (2021)
- [Multi-task manifold learning for small sample size datasets](https://mlsanity.com/paper/2111.11655/) (2021)

## Abstract (arXiv)

This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions. Furthermore, this latent space is endowed with a natural pull-back metric. The correspondences between conditions are obtained by minimizing an energy functional, resulting in diffeomorphism flows between fibers. We illustrate this approach using MNIST and Olivetti and benchmark its performances on the task of batch correction, which is the problem of integrating multiple biological datasets together.