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
地点
https://hkust.zoom.us/j/93244715329 (Passcode: 3485)
讲者/表演者
Prof. Zhenjie Ren
Université Paris-Dauphine
主办单位
Department of Mathematics
联系方法
付款详情
对象
Alumni, Faculty and staff, PG students, UG students
语言
英语
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