Recently there is a rising interest in the research of mean-field optimization, in particular because of its role in analyzing the training of neural networks. In this talk, by adding the Fisher Information (in other word, the Schrodinger kinetic energy) as the regularizer, we relate the mean-field optimization problem with a so-called mean field Schrodinger (MFS) dynamics. We develop a free energy method to show that the marginal distributions of the MFS dynamics converge exponentially quickly towards the unique minimizer of the regularized optimization problem. We shall see that the MFS is a gradient flow on the probability measure space with respect to the relative entropy. Finally, we propose a Monte Carlo method to sample the marginal distributions of the MFS dynamics. This is an ongoing joint work with Julien Claisse, Giovanni Conforti and Songbo Wang.

3月16日
4:30pm - 5:30pm
地點
https://hkust.zoom.us/j/93244715329 (Passcode: 3485)
講者/表演者
Prof. Zhenjie Ren
Université Paris-Dauphine
主辦單位
Department of Mathematics
聯絡方法
付款詳情
對象
Alumni, Faculty and staff, PG students, UG students
語言
英語
其他活動
5月11日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Regioselective Pyridine C-H-Functionalization and Skeletal Editing
Abstract Pyridines belong to the most abundant heteroarenes in medicinal chemistry and in agrochemical industry. In the lecture, highly regioselective pyridine C-H functionalization through a d...
1月20日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - A Journey to Defect Science and Engineering
Abstract A defect in a material is one of the most important concerns when it comes to modifying and tuning the properties and phenomena of materials. The speaker will review his study of defec...