Negar Safinianaini: Understanding Generative AI: Latent Space Issues and an Information-Geometric Approach

Abstract: Deep Neural Networks can represent a data distribution using latent variables and a nonlinear map from the latent space to the data space. Because this map is nonlinear, Euclidean distances in the latent space do not generally correspond to distances in the data space. We show how differential geometry can be used to account for this distortion and define a more appropriate geometry on the latent space. We demonstrate the approach on several standard datasets as well as on transitions between cancerous tumor states. The resulting geometry provides more meaningful paths through the latent space and leads to smoother interpolations than existing methods.