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

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.

کلیدواژه ها:

Graph Neural Networks ، Non-Euclidean Data ، Geometric Deep Learning ، Message Passing ، Graph Representation Learning