LENS: Learning & Exploitation of Latent Space Geometries

Motivation

Recent breakthroughs in machine learning and artificial intelligence—spanning images, video, text, and other complex data—can be traced to the hidden structure of real-world data spaces. Although an image is formally a point in the immense space of all pixel arrays, the subset of natural scenes occupies a relatively low-dimensional, smooth manifold. This manifold hypothesis has far-reaching implications: if we can model and exploit the geometry of such manifolds, we can achieve more efficient, robust, and interpretable learning and inference. Early manifold learning methods (Isomap, LLE, MDS) in the 1990s–2000s pioneered this view but were limited in scalability and expressiveness. Today, large datasets, powerful computation, and deep generative models—variational autoencoders (VAEs), generative adversarial networks (GANs), diffusion and flow-based models—offer a new opportunity: to learn manifolds directly in latent spaces where data are compactly represented. These advances invite a fresh synthesis of geometry, topology, and modern AI, enabling principled exploration of latent representations, their Riemannian structure, and their role in next-generation learning algorithms.

Invited Speakers

Tom Fletcher

University of Virginia

Yulia Gel

Virginia Tech University

Søren Hauberg

Technical University of Denmark

Virtual Talk

Michael Kirby

Colorado State University

René Vidal

University of Pennsylvania

Baba C. Vemuri

University of Florida

Laurent Younes

Johns Hopkins University