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

Understand

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.