مجله مدل‌سازی پیشرفته ریاضی

مجله مدل‌سازی پیشرفته ریاضی

Graph Neural Networks: Mathematical Foundations, Modern Architectures, and Future Directions

نوع مقاله : مقاله پژوهشی

نویسندگان
1 Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran, Iran.
2 Math Teacher, Department of Education, Tehran, Iran
چکیده
چکیده:

Graph Neural Networks (GNNs) have become a central framework for learning from graph-structured data, with applications in social networks, recommendation systems, molecular science, knowledge graphs, and scientific discovery. This survey reviews the mathematical foundations, architectural evolution, and emerging directions of GNNs in a compact and unified form. We discuss message passing, spectral graph theory, graph convolution, attention-based aggregation, expressivity, stability, and the main limitations of deep graph models. Representative architectures, including recurrent GNNs, GCN, GraphSAGE, MPNN, GAT, heterogeneous GNNs, graph transformers, and graph language models, are compared from the viewpoint of their design principles, strengths, limitations, and application domains. The survey also summarizes benchmark datasets, practical modeling considerations, and future challenges such as scalability, over-smoothing, over-squashing, uncertainty estimation, foundation models, and graph--language integration. The aim is to provide a concise reference that connects theory, architecture, and practice in modern graph representation learning.
کلیدواژه‌ها
موضوعات

دوره 16، شماره 2 - شماره پیاپی 42
تابستان 1405
صفحه 143-168

  • تاریخ دریافت 08 آذر 1404
  • تاریخ بازنگری 14 تیر 1405
  • تاریخ پذیرش 17 مرداد 1405