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SUMMARY:Score-based Pullback Riemannian Geometry: Extracting the Data Mani
 fold Geometry using Anisotropic Flows - Georgios Batzolis (University of C
 ambridge)
DTSTART:20251112T163000Z
DTEND:20251112T171000Z
UID:TALK239644@talks.cam.ac.uk
DESCRIPTION:This is the abstract: Data-driven Riemannian geometry has emer
 ged as a powerful tool for interpretable representation learning\, offerin
 g improved efficiency in downstream tasks. Moving forward\, it is crucial 
 to balance cheap manifold mappings with efficient training algorithms. In 
 this work\, we integrate concepts from pullback Riemannian geometry and ge
 nerative models to propose a framework for data-driven Rie- mannian geomet
 ry that is scalable in both geometry and learning: score-based pullback Ri
 emannian geometry. Focusing on unimodal distributions as a first step\, we
  propose a score-based Riemannian structure with closed-form geodesics tha
 t pass through the data probability density. With this struc- ture\, we co
 nstruct a Riemannian autoencoder (RAE) with error bounds for discovering t
 he correct data manifold dimension. This framework can naturally be used w
 ith anisotropic normalizing flows by adopting isometry regularization duri
 ng training. Through numerical experiments on diverse datasets\, including
  image data\, we demonstrate that the proposed framework produces high-qua
 lity geodesics passing through the data support\, reliably estimates the i
 ntrinsic dimension of the data manifold\, and provides a global chart of t
 he manifold. To the best of our knowledge\, this is the first scalable fra
 mework for extracting the complete geometry of the data manifold.
LOCATION:Seminar Room 1\, Newton Institute
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