Optimizing the Order of Modes in Tensor Train Decomposition

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00618543" target="_blank" >RIV/67985556:_____/25:00618543 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/49777513:23520/25:43976695

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/10930561" target="_blank" >https://ieeexplore.ieee.org/document/10930561</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/LSP.2025.3552005" target="_blank" >10.1109/LSP.2025.3552005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimizing the Order of Modes in Tensor Train Decomposition

Popis výsledku v původním jazyce

The tensor train (TT) is a popular way of representing high-dimensional hyper-rectangular data structures called tensors. It is widely used, for example, in quantum chemistry under the name „matrix product state“. The complexity of the TT model mainly depends on the bond dimensions that connect TT cores, constituting the model. Unlike canonical polyadic decomposition, the TT model complexity may depend on the order of the modes/indices in the data structures or the order of the core tensors in the TT, in general. This paper aims to provide methods for optimizing the order of the modes to reduce the bond dimensions. Since the number of possible orderings of the cores is exponentially high, we propose a greedy algorithm that provides a suboptimal solution. We consider three problem setups, i.e., specifications of the tensor: tensor given by a list of all its elements, tensor described by a TT model with some default order of the modes, and tensor obtained by sampling a multivariate function.

Název v anglickém jazyce

Optimizing the Order of Modes in Tensor Train Decomposition

Popis výsledku anglicky

The tensor train (TT) is a popular way of representing high-dimensional hyper-rectangular data structures called tensors. It is widely used, for example, in quantum chemistry under the name „matrix product state“. The complexity of the TT model mainly depends on the bond dimensions that connect TT cores, constituting the model. Unlike canonical polyadic decomposition, the TT model complexity may depend on the order of the modes/indices in the data structures or the order of the core tensors in the TT, in general. This paper aims to provide methods for optimizing the order of the modes to reduce the bond dimensions. Since the number of possible orderings of the cores is exponentially high, we propose a greedy algorithm that provides a suboptimal solution. We consider three problem setups, i.e., specifications of the tensor: tensor given by a list of all its elements, tensor described by a TT model with some default order of the modes, and tensor obtained by sampling a multivariate function.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA22-11101S" target="_blank" >GA22-11101S: Tenzorový rozklad v aktivní diagnostice poruch pro stochastické rozlehlé systémy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Signal Processing Letters

ISSN

1070-9908

e-ISSN

1558-2361

Svazek periodika

32

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

5

Strana od-do

1361-1365

Kód UT WoS článku

001455423000004

EID výsledku v databázi Scopus

2-s2.0-105001657523