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ACMD Seminar: Monotone Generative Modeling via a Gromov-Monge Embedding

Wonjun Lee
NIST-IMA Postdoctoral fellow, Institute for Mathematics and its Applications, University of Minnesota

Tuesday, Oct. 31, 2023, 1:00-2:00 PM MT (3:00-4:00 PM ET)

A video of this talk will be made available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page. It will be taken down from NISTube after 12 months at which point it can be requested by emailing the ACMD Seminar Chair.

Abstract: Generative Adversarial Networks (GANs) are powerful tools for creating new content, but they face challenges such as sensitivity to starting conditions and mode collapse. To address these issues, we propose a deep generative model that utilizes the Gromov-Monge embedding (GME). It helps identify the low-dimensional structure of the underlying measure of the data and then map it, while preserving its geometry, into a measure in a low-dimensional latent space, which is then optimally transported to the reference measure. We guarantee the preservation of the underlying geometry by the GME and c-cyclical monotonicity of the generative map, where c is an intrinsic embedding cost employed by the GME. The latter property is a first step in guaranteeing better robustness to initialization of parameters and mode collapse. Numerical experiments demonstrate the effectiveness of our approach in generating high-quality images, avoiding mode collapse, and exhibiting robustness to different starting conditions.

Bio: Wonjun Lee is a joint NIST-IMA Postdoctoral fellow in Analysis of Machine Learning at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota (UMN). He completed his Ph.D. at the University of California, Los Angeles in mathematics in 2022 under the guidance of Professor Stan Osher. Throughout his Ph.D., he has developed optimal transport-based algorithms to solve nonlinear partial differential equations (PDEs) such as Darcy’s law, tumor growth model, and mean field games. As a Postdoc, he is working with Professor Jeff Calder, Gilad Lerman, and Li Wang at UMN to develop PDE-based algorithms to solve high-dimensional machine learning problems and analyze the theoretical properties of the algorithms.

Host: Andrew Dienstfrey

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Note: Visitors from outside NIST must contact Lochi Orr (301) 975-3800; at least 24 hours in advance.

Created January 18, 2023, Updated June 11, 2024