Методы оптимизации обобщенных тензорных сверток

Методы оптимизации обобщенных тензорных сверток

Автор: Гареев Роман Альбертович

Журнал: Вестник Южно-Уральского государственного университета. Серия: Вычислительная математика и информатика @vestnik-susu-cmi

Статья в выпуске: 2 т.9, 2020 года.

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Свертка тензоров является одной из основных операций "Тензорного исчисления" - отдельного раздела математики, ставшего основным языком для описания фундаментальных законов таких областей науки, как теория относительности, механика, электродинамика и физика твердого тела. Эффективность выполнения свертки тензоров и её обобщений имеет существенную практическую значимость для таких областей как решение задач математической физики, машинного обучения, в спектральных методах, в квантовой химии, при интеллектуальном анализе данных, в высокопроизводительных вычислениях на многопроцессорных системах, и др. В последние двадцать лет количество методов оптимизации тензорных сверток значительно увеличилось и продолжает возрастать. В статье представлен обзор активно используемых подходов к оптимизации свертки тензоров, применяемых при решении прикладных задач на однопроцессорных и многопроцессорных вычислительных системах с распределенной памятью. В работе представлены методы оптимизации важных частных случаев свертки тензоров - матричного и матрично-векторного произведения, использующихся для большинства оптимизаций сверток тензоров. Описанные оптимазации могут применяться в процессе компиляции программ, выполняемой промышленными компиляторами. Представленная информация может помочь при систематизации уже имеющихся знаний.

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Свертка тензоров, линейная алгебра, высокопроизводительные вычисления

Короткий адрес: https://sciup.org/147234270

IDR: 147234270   |   DOI: 10.14529/cmse200202

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