Part IV · Ch. 11 — GNN (Graph Neural Network)

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Connectionist · Graphs · Message passing. Learns over graph-structured data (molecules, networks, maps). Card: ../02-types-of-ai/02-connectionist.kmd.

🎨 Figure F-IV.11.0 — Messages between neighbors. Brief: a graph with nodes exchanging messages (arrows) and updating their vectors; illustrate a molecule as an example.

GNN — message passing

1. Definition and short history

Generalizes neural networks to graphs, aggregating information from neighbors. A prominent application: a component of AlphaFold and drug discovery.

2. Foundations

  • Graph theory — structure, neighborhood, spectral (Laplacian).
  • Linear algebra — adjacency matrix, spectral convolution.
  • Group theory / symmetries — invariance to node permutation.
  • Chemistry/biology — molecules and proteins as graphs.

3. Algorithms and architectures

  • Message passing — each node aggregates messages from neighbors and updates state.
  • Variants — GCN (convolution), GAT (attention), GraphSAGE (sampling),

    MPNN.

  • Readout — aggregation for nodeedgegraph prediction.

4. Inputs

  • Hardware: GPU; large graphs require sampling/partitioning.
  • Data: labeled graphs (molecules, social networks, knowledge graphs).
  • Data structures: adjacency lists, sparse tensors.
  • Systems: PyG, DGL; neighborhood sampling for scale.

5. Specialized life cycle

Stage Specialization
0 Problem Nodeedgegraph prediction (molecular property, recommendation)
1 Data Build the graph (nodes, edges, features); labels
2 EDA Degree, components, homophily, class imbalance
3 Modeling GCNGATSAGE; depth (risk of over-smoothing)
4 Training Mini-batch via neighborhood sampling
5 Evaluation Nodeedge accuracyAUC; inductive generalization
5.5 Acceptance Robustness to graph perturbation, generalization to new graphs
6 Production Inference on dynamic graph; incremental update
7 Monitoring Drift in graph structure
8 Retraining New nodes/edges
9 Governance Privacy in social networks, relational bias

6. Capabilities, modes and modalities

Relational/structural: molecular property, recommendation, fraud detection, traffic/routing, knowledge graph reasoning.

7. Limits, risks and ethics

Over-smoothing with depth; scale on massive graphs; privacy in relational data; homophily bias.

8. State of the art and examples

AlphaFold (a component), GNNs for drug and material discovery, maps (ETA), industrial recommendation; convergence with Transformers (*graph transformers*).