195 citations · 196 across the 13 of their papers we have counts for
4 papers · 1 filter
Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor
Xun Tang, Nan Sheng, Lexing Ying
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting…
Solving high-dimensional Kolmogorov backward equations with functional hierarchical tensor operators
Xun Tang, Leah Collis, Lexing Ying
Solving high-dimensional partial differential equations necessitates methods free of exponential scaling in the dimension of the problem. This work introduces a tensor network appr…
A Sinkhorn-type Algorithm for Constrained Optimal Transport
Xun Tang, Holakou Rahmanian, Michael Shavlovsky +3
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distan…
Accelerating Sinkhorn Algorithm with Sparse Newton Iterations
Xun Tang, Michael Shavlovsky, Holakou Rahmanian +4
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization a…