ntvНаучно-технический вестник информационных технологий, механики и оптикиScientific and Technical Journal of Information Technologies, Mechanics and Optics2226-14942500-0373Университет ИТМО10.17586/2226-1494-2026-26-1-77-84ntv-566Research ArticleКОМПЬЮТЕРНЫЕ СИСТЕМЫ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИCOMPUTER SCIENCEВыбор полиномиальных функций в сетях Колмогорова–Арнольда для сегментации медицинских изображений в условиях малых выборокPolynomial function selection in Kolmogorov-Arnold Networks for medical image segmentation with limited datahttps://orcid.org/0009-0007-8551-1908МанжосГ. Ю.ManzhosG. Yu.

Манжос Геннадий Юрьевич — аспирант, ассистент

Нижний Новгород, 603005

Санкт-Петербург, 197101

Gennadiy Yu. Manzhos — PhD Student, Assistan

Nizhniy Novgorod, 603005

Saint Petersburg, 197101

manzhos_gy@pimunn.nethttps://orcid.org/0000-0003-1886-2867ТомиловИ. В.TomilovI. V.

Томилов Иван Вячеславович — старший лаборант

Санкт-Петербург, 197101

sc 57772599000

Ivan V. Tomilov — Senior Laboratory Assistant

Saint Petersburg, 197101

sc 57772599000

ivan-tomilov3@yandex.ruhttps://orcid.org/0000-0002-1361-6037ГусароваН. Ф.GusarovaN. F.

Гусарова Наталия Федоровна — кандидат технических наук,старший научный сотрудник, доцент

Санкт-Петербург, 197101

sc 57162764200

Natalia F. Gusarova — PhD, Senior Researcher, Associate Professor

Saint Petersburg, 197101

sc 57162764200

nfgusarova@itmo.ruhttps://orcid.org/0000-0001-5345-5461ВалитоваЮ. О.ValitovaYu. O.

Валитова Юлия Олеговна — кандидат педагогических наук, доцент

Санкт-Петербург, 197101

Yulia O. Valitova — PhD (Education), Associate Professor

Saint Petersburg, 197101

yulia.o.valitova@itmo.ruПриволжский исследовательский медицинский университет; Университет ИТМОРоссияPrivolzhsky Research Medical University; ITMO UniversityRussian FederationУниверситет ИТМОРоссияITMO UniversityRussian Federation2026250220262617784Copyright © Манжос Г.Ю., Томилов И.В., Гусарова Н.Ф., Валитова Ю.О., 20262026Манжос Г.Ю., Томилов И.В., Гусарова Н.Ф., Валитова Ю.О.Manzhos G.Y., Tomilov I.V., Gusarova N.F., Valitova Y.O.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ntv.elpub.ru/jour/article/view/566

Введение. Современные методы обработки медицинских изображений в большей части основаны на сверточных нейронных сетях и архитектурах трансформер. Главной проблемой является значительный объем параметров существующих моделей нейронных сетей, что ведет к высоким требованиям к вычислительным ресурсам диагностических медицинских систем. Метод. Сети Колмогорова–Арнольда, построенные на основе сплайнфункций, демонстрируют сопоставимую точность с традиционными архитектурами, при этом имеют значительно меньшее число параметров. В сверточных слоях сети Колмогорова–Арнольда возможно использование различных базисных полиномиальных функций вместо сплайнов, что существенно влияет на качество сегментации. В работе представлено сравнение эффективности 22 различных полиномиальных функций в сети Колмогорова–Арнольда при сегментации двухмерных медицинских изображений на малых выборках.Основные результаты. Экспериментальные данные показали, что исследуемые полиномиальные функции достигают производительности, сопоставимой с передовыми моделями трансформер при значительно меньшем количестве параметров. Обсуждение. Полученные результаты подтверждают перспективность дальнейшего изучения полиномиальных функций в архитектуре сверточных блоков сетей Колмогорова–Арнольда, особенно при ограниченных вычислительных ресурсах. Необходимы дальнейшие исследования полиномиальных функций в сверточных слоях сети Колмогорова–Арнольда в задачах обработки высокотехнологичных медицинских изображений.

Modern methods for processing medical images are mostly based on convolutional neural networks and transformer architectures. A major issue is the large number of parameters in existing neural network models, which leads to high computational resource requirements. Kolmogorov-Arnold Networks, built upon spline functions, demonstrate comparable accuracy to traditional architectures while having significantly fewer parameters. In the convolutional layers of Kolmogorov-Arnold Networks, various polynomial basis functions can be used instead of splines, which substantially affect segmentation quality. The objective of this study is to compare the effectiveness of 22 different polynomial functions within Kolmogorov-Arnold Networks for segmenting two-dimensional medical images on small datasets. Experimental results show that the polynomial functions studied achieve performance comparable to state-ofthe-art transformer models while requiring significantly fewer parameters. The obtained results confirm the promising potential of further research into polynomial functions within the convolutional blocks of Kolmogorov-Arnold Networks, especially under limited computational resources. Further studies of polynomial functions in the convolutional layers of Kolmogorov-Arnold Networks are necessary for processing advanced medical imaging data.

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The authors declare that there are no conflicts of interest present.