Informacionnye TehnologiiInformacionnye TehnologiiИнформационные технологии1684-6400New Technologies Publishing House70226710.17587/it.31.291-307Neural network technologiesНейросетевые технологииReview ArticleGraph neural networks and their extensions based on hyperbolic geometry: a reviewГрафовые нейронные сети и их расширение на основе гиперболической геометрии: обзорPetrenkoP. B.ПетренкоП. Б.
Russian Federation

Dr. of Tech. Sc., Professor, Signal Processing Center

д-р техн. наук, проф., член-корр. Российской инженерной академии, Центр обработки сигналов

prof.petrenko54@gmail.comTolpyginА. S.ТолпыгинА. С.
Russian Federation

Cand. of Tech. Sc.

канд. техн. наук, доц.

tolpygin@bmstu.ruSynergy Design BureauКБ "Синергия"Bauman Moscow State Technical UniversityМГТУ им. Н. Э. Баумана1506202531629130706022026Copyright ©; 2025, Informacionnye TehnologiiCopyright ©; 2025, Информационные технологии2025Informacionnye TehnologiiИнформационные технологииhttps://journals.eco-vector.com/1684-6400/article/view/702267

Graph neural networks generalize traditional neural networks for graph-structured data and have attracted wide attention due to their impressive capabilities. They are in demand in machine learning, as they can work with heterogeneous information, help to identify relationships between events and data, provide robustness to incomplete, unclear and noisy data, allow to analysis of large amounts of data and structures in the form of knowledge graphs. Training of graph neural networks in hyperbolic space has gained popularity in recent years due to their ability to model graphs with hidden hierarchical data, and because they are more compact and denser. The purpose of applying non-Euclidean geometry theory in modifying graph neural networks is to ensure their stability and better performance compared to Euclidean neural networks. The review of research and development is devoted to the analysis of modern achievements in the field of graph neural networks creation and consideration of accompanying problems. Particular attention is paid to the issues of graph embedding and their representation in non-Euclidean space. This is due to the fact that the performance of models is largely determined by the embedding algorithms and the choice of geometric space for representing graph structures. The prospectivity and efficiency of this approach have been confirmed by works on the creation of hyperbolic convolutional networks of graphs with the property of controlling the curvature of the space in each layer. At the same time, today there is a need for a more detailed consideration of the possibilities of graph neural networks based on the application of methods of hyperbolic geometry because of the insufficient attention paid to these issues in the domestic literature.

Графовые нейронные сети обобщают традиционные нейронные сети для данных с графовой структурой и привлекают широкое внимание благодаря своим впечатляющим возможностям. Они востребованы в машинном обучении, так как позволяют работать c разнородной информацией, способствуют выявлению взаимосвязей между событиями и данными, обеспечивают устойчивость к неполным, нечетким и зашумленным данным, позволяют проводить анализ большого объема данных и структур в виде графов знаний.

Обучение графовых нейронных сетей в гиперболическом пространстве приобрело популярность в последние годы благодаря их способности моделировать графы со скрытыми иерархическими данными, а также вследствие того, что они более компактны и плотны. Цель применения неевклидовой геометрии для расширения графовых нейронных сетей состоит в обеспечении их высокой точности и лучшей производительности в сравнении с евклидовыми нейронными сетями.

Обзор исследований и разработок посвящен анализу современных достижений в области создания графовых нейронных сетей и рассмотрению сопутствующих этому проблем. Особое внимание уделено вопросам встраивания графов и их представлению в неевклидовом пространстве. Это обусловлено тем, что производительность моделей во многом определяется алгоритмами встраивания и выбором геометрического пространства для представления графовых структур. Перспективность и эффективность этого подхода подтвердили работы по созданию гиперболических сверточных сетей графов, обладающих свойством управления кривизной пространства в каждом слое. Вместе с этим, сегодня возникает потребность более подробного рассмотрения возможностей графовых нейронных сетей на основе применения методов гиперболической геометрии из-за недостаточного внимания, уделяемого этим вопросам в отечественной литературе.

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