AI & Fundamentals

Entropy-regularized optimal transport and its connection with score estimation - Soumik Pal, Professor, University of Washington

Abstract:

Entropy-regularized optimal transport (EOT) is a popular version of the classical Monge-Kantorovich optimal transport problem. The addition of entropy as a regularizer was introduced to provide smoothness, robustness, and computational efficiency. But, in fact, it does so much more. I will focus on one striking aspect, its connection with estimating the so-called score function (the gradient of the log density with respect to the argument). As an application we will talk about discretizing Wasserstein gradient flows by an iterated application of EOT. This last application is motivated by the work of Sanders et al on a modification of the transformer network model that they called Sinkformer. No prior knowledge of entropy-regularized OT or Schrödinger bridges is required. 

Bio

Soumik Pal is a Professor and the Robert B. Warfield, Jr., Endowed Faculty Fellow in the Department of Mathematics at the University of Washington. He also holds adjunct professorships at the Department of Applied Mathematics and the Department of Statistics. His research interests are in probabilistic and statistical aspects of Monge-Kantorovich optimal transport theory. His other interests include mean-filed interacting particle systems, random graphs, and mathematical finance.