195 citations · 196 across the 13 of their papers we have counts for
15 papers
Variational inference and density estimation with non-negative tensor of hierarchical tucker format
Xun Tang, Haoxuan Chen, Lexing Ying
In this work, we present an efficient method to compress a high-dimensional discrete probability function, i.e., a probability tensor, into a non-negative hierarchical Tucker forma…
Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State
Xun Tang, Haoxuan Chen, Yuehaw Khoo +1
We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure ap…
An efficient algorithm for entropic optimal transport under martingale-type constraints
Xun Tang, Michael Shavlovsky, Holakou Rahmanian +2
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete marting…
Variational inference and density estimation with non-negative tensor train
Xun Tang, Rajat Dwaraknath, Lexing Ying
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings…
On a spherically lifted spin model at finite temperature
Xun Tang, Yuehaw Khoo, Lexing Ying
We investigate an \(n\)-vector model over \(k\) sites with generic pairwise interactions and spherical constraints. The model is a lifting of the Ising model whereby the support of…
Initialization and training of matrix product state probabilistic models
Xun Tang, Yuehaw Khoo, Lexing Ying
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a…
Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor
Xun Tang, Lexing Ying
We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model de…
Wavelet-based density sketching with functional hierarchical tensor
Xun Tang, Lexing Ying
We introduce the functional hierarchical tensor under a wavelet basis (FHT-W) ansatz for high-dimensional density estimation in lattice models. Recently, the functional tensor netw…
Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors
Nan Sheng, Xun Tang, Haoxuan Chen +1
The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant ca…
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…
Solving high-dimensional Fokker-Planck equation with functional hierarchical tensor
Xun Tang, Lexing Ying
This work is concerned with solving high-dimensional Fokker-Planck equations with the novel perspective that solving the PDE can be reduced to independent instances of density esti…
Solving parametric PDE problems with artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random…