GNn

Graph neural networks (GNNs) are a family of neural networks designed to operate on graph-structured data. They leverage the irregular topology of graphs by iteratively aggregating information from a node's neighbors to update its representation, producing node, edge, or graph-level embeddings that capture structural and feature information.

A common formulation is the message passing or neural message passing framework, where each layer computes messages from neighboring nodes, aggregates them, and applies a nonlinear transformation. Notable architectures include Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Isomorphism Networks (GINs), and more general graph neural networks (MPNNs). These models differ in how they define neighborhood aggregation and parameterization.

GNNs are trained end-to-end in supervised, semi-supervised, or unsupervised settings and are used for tasks such as node classification, link prediction, and graph classification. Training can be challenged by large graphs, necessitating sampling or mini-batching, and by phenomena like over-smoothing in deep stacks.

Applications span social networks, chemistry and materials science, biology, recommender systems, and knowledge graphs. Standard benchmarks include citation networks (Cora, Citeseer, PubMed) and graph classifications datasets (PROTEINS, D&D, QM9). Evaluation uses accuracy, F1, ROC-AUC, or regression error depending on task.

Ongoing research addresses scalability to large and dynamic or heterogeneous graphs, inductive versus transductive learning, interpretability, robustness to noise, and integration with multimodal data.