Custom Research VAE (purpose-built variational autoencoder for representation-geometry studies)

various (academic)

Structures found in this family (1)

Curvature profile of the representation manifold

By model (5)

MLP/convolutional VAE, trained on MNIST digit subsets and video frames (Arvanitidis, Hansen & Hauberg)

Curvature profile of the representation manifold

VAE trained on Galaxy Zoo 64 imagery (Ascarate, Lebrat, Santa Cruz, Fookes & Salvado)

Curvature profile of the representation manifold

VAE trained on Mars Rover Mastcam imagery (Ascarate, Lebrat, Santa Cruz, Fookes & Salvado)

Curvature profile of the representation manifold

Convolutional VAE (32-dim latent), trained on CelebA and SVHN (Shao, Kumar & Fletcher)

Curvature profile of the representation manifold

Vanilla VAE and disentangling VAE variants (Szabo et al., Mathieu et al., Jha et al.), trained on MNIST, MultiPIE and 3D Chairs (Shukla, Bhagat, Anand & Turaga)

Curvature profile of the representation manifold

Observations (4)

A real VAE's decoder-induced pullback metric and its geodesics substantially improve interpolation and density estimation over naive Euclidean latent distance

Real trained VAE latent spaces organize into measurably distinct ordered, disordered, and glassy phases, and shifting toward a more ordered phase improves anomaly detection

Real CelebA- and SVHN-trained VAE manifolds are surprisingly close to zero curvature, so linear latent interpolation nearly matches true geodesics

Class-distinguishing latent regions of real disentangled VAE variants carry measurably higher pullback-metric curvature than a vanilla VAE's latent space

Papers

Latent Space Oddity: On the Curvature of Deep Generative Models (2018), High-Dimensional Latents Should Be Diagnosed Through Phase Structure (2026), The Riemannian Geometry of Deep Generative Models (2018), Geometry of Deep Generative Models for Disentangled Representations (2018)