-
1
Tensor Algebras in Finite Tensor Categories
Published 2021“…We work within the broader framework of finite (multi-)tensor categories $\mathcal{C}$, classifying tensor algebras in $\mathcal{C}$ in terms of $\mathcal{C}$-module categories. …”
Get full text
Article -
2
-
3
-
4
Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
Published 2021“…We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. …”
Get full text
Article -
5
-
6
The tensor algebra compiler
Published 2021“…<jats:p>Tensor algebra is a powerful tool with applications in machine learning, data analytics, engineering and the physical sciences. …”
Get full text
Article -
7
-
8
Spectral Tensor-Train Decomposition
Published 2017“…We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. …”
Get full text
Get full text
Get full text
Article -
9
-
10
Optimal recovery of tensor slices
Published 2021“…Viewing the matrix we seek to recover and the side information we have as slices of a tensor, we consider the problem of Slice Recovery, which is to recover specific slices of a tensor from noisy observations of the tensor. …”
Get full text
Article -
11
Themes in numerical tensor calculus
Published 2022“…This thesis studies several distinct, but related, aspects of numerical tensor calculus. First, we introduce a simple, black-box compression format for tensors with a multiscale structure. …”
Get full text
Thesis -
12
-
13
Loop Optimization for Tensor Network Renormalization
Published 2017“…We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. …”
Get full text
Get full text
Article -
14
-
15
Tensor factorization toward precision medicine
Published 2019“…In this opinion article, we analyze the modest literature on applying tensor factorization to various biomedical fields including genotyping and phenotyping. …”
Get full text
Article -
16
Multiresolution Low-rank Tensor Formats
Published 2021“…We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale, and we show how this leads to an increase in compression for a fixed accuracy. …”
Get full text
Article -
17
Multiresolution Low-rank Tensor Formats
Published 2022“…We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale, and we show how this leads to an increase in compression for a fixed accuracy. …”
Get full text
Article -
18
On algorithms for and computing with the tensor ring decomposition
Published 2021“…© 2020 John Wiley & Sons, Ltd. Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension instead of exponential scaling. …”
Get full text
Article -
19
-
20
Spectral methods from tensor networks
Published 2021“…Publication rights licensed to ACM. A tensor network is a diagram that specifies a way to “multiply” a collection of tensors together to produce another tensor (or matrix). …”
Get full text
Article