4 papers
Iso-Riemannian Optimization on Learned Data Manifolds
Willem Diepeveen, Melanie Weber
We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradien…
Protein Graph Neural Networks for Heterogeneous Cryo-EM Reconstruction
Jonathan Krook, Axel Janson, Joakim Andén +2
We present a geometry-aware method for heterogeneous single-particle cryogenic electron microscopy (cryo-EM) reconstruction that predicts atomic backbone conformations. To incorpor…
Neural Feature Geometry Evolves as Discrete Ricci Flow
Moritz Hehl, Max von Renesse, Melanie Weber
Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our under…
Automated Manifold Learning for Reduced Order Modeling
Imran Nasim, Melanie Weber
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across sc…