The Riemannian Geometry of Deep Generative Models

Understand

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space.

• Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space.
• In this paper, we investigate the Riemannian geometry of these generated manifolds.
• First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold.