Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes

The main problem of artificial intelligence is increasing productivity and quality of problem solutions. Due to the growing architecture of modern neural networks, one needs to engage advanced mathematical methods. Deep learning models use more hardware resources, which increases the computational c...

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Главные авторы:	Abdulsalyamova, A. S., Абдулсалямова, А. Ш., Abdulkadirov, R. I., Абдулкадиров, Р. И., Lyakhov, P. A., Ляхов, П. А., Nagornov, N. N., Нагорнов, Н. Н.
Формат:	Статья
Язык:	English
Опубликовано:	Springer Science and Business Media Deutschland GmbH 2024
Темы:	Strassen method Strassen-Winograd method Comparative analysis Computational complexity Decreasing time consumption Matrix multiplication
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29206
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id	ir-123456789-29206
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spelling	ir-123456789-292062024-11-05T11:23:41Z Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes Abdulsalyamova, A. S. Абдулсалямова, А. Ш. Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Nagornov, N. N. Нагорнов, Н. Н. Strassen method Strassen-Winograd method Comparative analysis Computational complexity Decreasing time consumption Matrix multiplication The main problem of artificial intelligence is increasing productivity and quality of problem solutions. Due to the growing architecture of modern neural networks, one needs to engage advanced mathematical methods. Deep learning models use more hardware resources, which increases the computational complexity. Therefore, it is necessary to apply modifications of machine learning models at a fundamental level using alternative matrix multiplication methods. This article proposes a comparative analysis of the computational complexity of matrix multiplication implemented by the standard Strassen and Strassen-Winograd methods. We consider data time complexity for int32, int64, float32, and float64 data types. In addition, the number of recursions for each matrix size is determined. According to the experimental results, we can conclude that the Strassen-Winograd matrix multiplication method has minimal time costs compared to the Strassen method and standard approaches by 3%–6% and 30%–40%, respectively. It is possible to incorporate such an approach into convolutional, spike, and auto-encoding layers. 2024-11-05T11:22:06Z 2024-11-05T11:22:06Z 2024 Статья Abdulsalyamova A., Abdulkadirov R., Lyakhov P., Nagornov N. Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes // Lecture Notes in Networks and Systems. - 2024. - 1044 LNNS. - pp. 432 - 438. - DOI: 10.1007/978-3-031-64010-0_40 https://dspace.ncfu.ru/handle/123456789/29206 en Lecture Notes in Networks and Systems application/pdf Springer Science and Business Media Deutschland GmbH
institution	СКФУ
collection	Репозиторий
language	English
topic	Strassen method Strassen-Winograd method Comparative analysis Computational complexity Decreasing time consumption Matrix multiplication
spellingShingle	Strassen method Strassen-Winograd method Comparative analysis Computational complexity Decreasing time consumption Matrix multiplication Abdulsalyamova, A. S. Абдулсалямова, А. Ш. Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Nagornov, N. N. Нагорнов, Н. Н. Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
description	The main problem of artificial intelligence is increasing productivity and quality of problem solutions. Due to the growing architecture of modern neural networks, one needs to engage advanced mathematical methods. Deep learning models use more hardware resources, which increases the computational complexity. Therefore, it is necessary to apply modifications of machine learning models at a fundamental level using alternative matrix multiplication methods. This article proposes a comparative analysis of the computational complexity of matrix multiplication implemented by the standard Strassen and Strassen-Winograd methods. We consider data time complexity for int32, int64, float32, and float64 data types. In addition, the number of recursions for each matrix size is determined. According to the experimental results, we can conclude that the Strassen-Winograd matrix multiplication method has minimal time costs compared to the Strassen method and standard approaches by 3%–6% and 30%–40%, respectively. It is possible to incorporate such an approach into convolutional, spike, and auto-encoding layers.
format	Статья
author	Abdulsalyamova, A. S. Абдулсалямова, А. Ш. Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Nagornov, N. N. Нагорнов, Н. Н.
author_facet	Abdulsalyamova, A. S. Абдулсалямова, А. Ш. Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Nagornov, N. N. Нагорнов, Н. Н.
author_sort	Abdulsalyamova, A. S.
title	Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
title_short	Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
title_full	Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
title_fullStr	Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
title_full_unstemmed	Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes
title_sort	comparative analysis of fast matrix multiplication methods on different datatypes
publisher	Springer Science and Business Media Deutschland GmbH
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29206
work_keys_str_mv	AT abdulsalyamovaas comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT abdulsalâmovaaš comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT abdulkadirovri comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT abdulkadirovri comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT lyakhovpa comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT lâhovpa comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT nagornovnn comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes AT nagornovnn comparativeanalysisoffastmatrixmultiplicationmethodsondifferentdatatypes
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Comparative Analysis of Fast Matrix Multiplication Methods on Different Datatypes

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