Week 0: Orientation Week

Part 1: Foundations & Core Architectures

Week 1: Graph Foundations & Traditional Embeddings

  • Basic graph concepts (nodes, edges, adjacency/sparse matrix representation).
  • Centrality measurements (Degree, Betweenness, PageRank, etc.) and Graph kernels.
  • Shallow embedding models: Random walk (DeepWalk, Node2Vec, etc.) and proximity-based models.

Week 2: Message Passing & Graph Neural Networks

  • Motivation from CNNs to GNNs.
  • The Message Passing Neural Network (MPNN) framework.
  • Graph Convolutional Networks (GCNs).

Week 3: Theoretical Foundations & Expressivity

  • The limitations of message passing.
  • The Weisfeiler-Lehman (1-WL) Isomorphism Test.
  • Higher-order GNNs and Subgraph GNNs.

Week 4: Scalability of Graph Neural Networks

  • Issues with large-scale graph training (neighborhood explosion).
  • Node-wise sampling (GraphSAGE).
  • Graph/Subgraph-wise sampling (ClusterGCN, GraphSAINT).

Part 2: Bottlenecks, Scalability & Trust

Week 5: Training Deeper GNNs

  • What impedes deep GNNs?
  • Over-smoothing vs. Over-squashing.
  • Under-Reaching
  • Multi-hop Aggregation:
    • Explicit hop-wise aggregation: MixHop, SIGN.
    • Adaptive hop propagation: GPR-GNN, APPNP.
    • Layer-wise / jump aggregation: Jumping Knowledge (JKNet).

Week 6: Heterophily, Graph Structure Learning

  • Homophily vs. Heterophily: revisiting the smoothness assumption; heterophily-aware GNNs (H2GCN, GPR-GNN).
  • Graph Structure Learning (GSL): jointly or adaptively learning graph topology and node representations.

Week 7: Attentive GNNs and Graph Pooling

  • Graph Attention Networks (GAT) and Attention in Heterogeneous graphs.
  • Hierarchical Graph Pooling (DiffPool, SAGPool).

Week 8: Mid-Term Exam

Week 9: Explainability, Generalizability and Robustness

  • Interpreting GNN predictions (GNNExplainer, PGExplainer).
  • Adversarial attacks on graph data (modifying edges/features).
  • Defenses and robust GNN architectures.

Part 3: Advanced Architectures & Generative Models

Week 10: Graph Transformers

  • From Message Passing to Self-Attention.
  • The necessity of Positional and Structural Encoding (PE/SE) in graphs.
  • Representative models (Graphormer, SAN).

Week 11: Generative Graph Models & Diffusion

  • Variational Autoencoders for graphs (VGAE).
  • Graph Diffusion Models (generating novel molecular structures or networks).

Week 12: Spatio-temporal Graph Neural Networks (STGNN)

  • Introduction to spatial + temporal dependencies.
  • Applications: Traffic forecasting, weather modeling, and action recognition.

Part 4: Cutting-Edge Applications & Synergies

Week 13: GNNs for Recommendation & Molecular Structure Learning

  • Bipartite graphs and user-item interactions; LightGCN and PinSage; RecSys evaluation metrics (condensed overview).
  • Molecules as graphs; Equivariant GNNs (E(n) Equivariance for 3D modeling).
  • Connections to AlphaFold and modern drug discovery.

Week 14: Heterogeneous Graphs, KGs, and GraphRAG

  • Knowledge Graph representation learning (TransE, RotatE).
  • Synergy with LLMs: Graph Retrieval-Augmented Generation (GraphRAG).

Week 15: Course Consolidation

Week 16: Final Exam