TALK: Conformal Generative Modeling
Speaker
Victor Dorobantu
Caltech
Host
Justin Solomon
CSAIL MIT
Zoom Link: https://caltech.zoom.us/j/83217864706?pwd=TVFhUGRSZmNFRXZEbWNGQlhsWWVqQT09
Abstract: Generative models can offer solutions to many scientific and engineering problems on manifolds, including novel data generation, stochastic optimization, and inverse problems. Many generative modeling approaches for data on Riemannian manifolds have been developed in recent years; however, relatively few existing methods can be used for data on arbitrary 2D surfaces or inside 3D volumes. We make use of tools from computational geometry (specifically conformal geometry) to simplify data domains, after which many generative modeling methods are available for use as plug-and-play subroutines. We show how to account for area distortion and its effect on log-likelihood training, as well as how to use multiple distinct meshes as data sources for a single common model. We demonstrate our framework on several complex manifolds and multiple generative modeling subroutines.
Bio: Victor Dorobantu is a PhD student at the California Institute of Technology (Caltech) in the Department of Computing and Mathematical Sciences (CMS), working with Professor Yisong Yue. His research interests tie together machine learning and geometry, with applications in generative modeling, convex optimization, control, and robotics.
Abstract: Generative models can offer solutions to many scientific and engineering problems on manifolds, including novel data generation, stochastic optimization, and inverse problems. Many generative modeling approaches for data on Riemannian manifolds have been developed in recent years; however, relatively few existing methods can be used for data on arbitrary 2D surfaces or inside 3D volumes. We make use of tools from computational geometry (specifically conformal geometry) to simplify data domains, after which many generative modeling methods are available for use as plug-and-play subroutines. We show how to account for area distortion and its effect on log-likelihood training, as well as how to use multiple distinct meshes as data sources for a single common model. We demonstrate our framework on several complex manifolds and multiple generative modeling subroutines.
Bio: Victor Dorobantu is a PhD student at the California Institute of Technology (Caltech) in the Department of Computing and Mathematical Sciences (CMS), working with Professor Yisong Yue. His research interests tie together machine learning and geometry, with applications in generative modeling, convex optimization, control, and robotics.