21 citations · 22 across the 4 of their papers we have counts for
5 papers · 1 filter
Efficient Optimal Transport Algorithm by Accelerated Gradient descent
Dongsheng An, Na Lei, Xianfeng Gu
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems…
Mode Collapse and Regularity of Optimal Transportation Maps
Na Lei, Yang Guo, Dongsheng An +4
This work builds the connection between the regularity theory of optimal transportation map, Monge-Ampère equation and GANs, which gives a theoretic understanding of the major draw…
Latent Space Optimal Transport for Generative Models
Huidong Liu, Yang Guo, Na Lei +4
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the pos…
Geometric Understanding of Deep Learning
Na Lei, Zhongxuan Luo, Shing-Tung Yau +1
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conv…
A Geometric View of Optimal Transportation and Generative Model
Na Lei, Kehua Su, Li Cui +2
In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a co…