Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps

Konstantin Usevich; Yassine Zniyed; Mariya Ishteva; Philippe Dreesen; André L. F. de Almeida

doi:10.23919/EUSIPCO58844.2023.10289900

Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps

Konstantin Usevich, Yassine Zniyed, Mariya Ishteva, Philippe Dreesen, André L. F. de Almeida

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

In this paper, we introduce a new decomposition of multivariate maps that generalizes the decoupling problem recently proposed in the system identification community. In the context of neural networks, this decomposition can be seen as a two-layer feedforward network with flexible activation functions. We show that for such maps the Jacobian and Hessian tensors admit Para Tuck and CP decompositions respectively. We propose a methodology to perform the two-layer decoupling of the given polynomial maps based on joint Para Tuck and CP decomposition, by combining first and second-order information.

Original language	English
Title of host publication	2023 31st European Signal Processing Conference (EUSIPCO)
Publisher	The IEEE
Pages	655-659
Number of pages	5
ISBN (Print)	979-8-3503-2811-0
DOIs	https://doi.org/10.23919/EUSIPCO58844.2023.10289900
Publication status	Published - 8 Sept 2023
Event	2023 31st European Signal Processing Conference (EUSIPCO) - Helsinki, Finland Duration: 4 Sept 2023 → 8 Sept 2023 http://eusipco2023.org/

Conference

Conference	2023 31st European Signal Processing Conference (EUSIPCO)
Abbreviated title	EUSIPCO 2023
Country/Territory	Finland
City	Helsinki
Period	4/09/23 → 8/09/23
Internet address	http://eusipco2023.org/

Keywords

Jacobian matrices
Tensors
Europe
Signal processing
System identification
Feedforward neural networks

Access to Document

10.23919/EUSIPCO58844.2023.10289900

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10289900

Cite this

@inproceedings{f33b951156d64a55ae6b0f1238621ebf,

title = "Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps",

abstract = "In this paper, we introduce a new decomposition of multivariate maps that generalizes the decoupling problem recently proposed in the system identification community. In the context of neural networks, this decomposition can be seen as a two-layer feedforward network with flexible activation functions. We show that for such maps the Jacobian and Hessian tensors admit Para Tuck and CP decompositions respectively. We propose a methodology to perform the two-layer decoupling of the given polynomial maps based on joint Para Tuck and CP decomposition, by combining first and second-order information.",

keywords = "Jacobian matrices, Tensors, Europe, Signal processing, System identification, Feedforward neural networks",

author = "Konstantin Usevich and Yassine Zniyed and Mariya Ishteva and Philippe Dreesen and Almeida, {Andr{\'e} L. F. de}",

year = "2023",

month = sep,

day = "8",

doi = "10.23919/EUSIPCO58844.2023.10289900",

language = "English",

isbn = "979-8-3503-2811-0",

pages = "655--659",

booktitle = "2023 31st European Signal Processing Conference (EUSIPCO)",

publisher = "The IEEE",

note = "2023 31st European Signal Processing Conference (EUSIPCO), EUSIPCO 2023 ; Conference date: 04-09-2023 Through 08-09-2023",

url = "http://eusipco2023.org/",

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TY - GEN

T1 - Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps

AU - Usevich, Konstantin

AU - Zniyed, Yassine

AU - Ishteva, Mariya

AU - Dreesen, Philippe

AU - Almeida, André L. F. de

PY - 2023/9/8

Y1 - 2023/9/8

N2 - In this paper, we introduce a new decomposition of multivariate maps that generalizes the decoupling problem recently proposed in the system identification community. In the context of neural networks, this decomposition can be seen as a two-layer feedforward network with flexible activation functions. We show that for such maps the Jacobian and Hessian tensors admit Para Tuck and CP decompositions respectively. We propose a methodology to perform the two-layer decoupling of the given polynomial maps based on joint Para Tuck and CP decomposition, by combining first and second-order information.

AB - In this paper, we introduce a new decomposition of multivariate maps that generalizes the decoupling problem recently proposed in the system identification community. In the context of neural networks, this decomposition can be seen as a two-layer feedforward network with flexible activation functions. We show that for such maps the Jacobian and Hessian tensors admit Para Tuck and CP decompositions respectively. We propose a methodology to perform the two-layer decoupling of the given polynomial maps based on joint Para Tuck and CP decomposition, by combining first and second-order information.

KW - Jacobian matrices

KW - Tensors

KW - Europe

KW - Signal processing

KW - System identification

KW - Feedforward neural networks

UR - https://ieeexplore.ieee.org/document/10289900/

U2 - 10.23919/EUSIPCO58844.2023.10289900

DO - 10.23919/EUSIPCO58844.2023.10289900

M3 - Conference article in proceeding

SN - 979-8-3503-2811-0

SP - 655

EP - 659

BT - 2023 31st European Signal Processing Conference (EUSIPCO)

PB - The IEEE

T2 - 2023 31st European Signal Processing Conference (EUSIPCO)

Y2 - 4 September 2023 through 8 September 2023

ER -

Tensor-Based Two-Layer Decoupling of Multivariate Polynomial Maps

Abstract

Conference

Keywords

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