Course Modules and Lecture Flow
Module I : Mathematical Foundations
Lecture 1: Graphs as Relational Inductive Bias
Why Euclidean ML fails on relational systems
Symmetry and permutation equivariance
Graphs vs manifolds
Applications across domains
Lecture 2: Matrix Analysis for Graph ML
Graph matrices, PSD matrices, Spectral decomposition, Rayleigh quotient, Eigenvalue inequalities
Lecture 3: Probability and Inference on Graphs
Probabilistic graphical models, Markov properties, Energy-based formulations
Lecture 4: Optimization Foundations
PART II — Spectral and Geometric Foundations
Lecture 5: Spectral Graph theory
Lecture 6: Smoothness and Dirichlet Energy
Lecture 7: Graph Fourier Analysis
Lecture 8: Diffusion and Heat Kernels
Lecture 9: Laplace–Beltrami Operator
Lecture 10: Graph Signal Processing
PART III — Representation Learning on Graphs
Lecture 11: Spectral Embeddings
Lecture 12: Random Walk Representation Learning
Lecture 13: Matrix Factorization Perspectives
Lecture 14: Self-Supervised and Contrastive Learning
Contrastive objectives
InfoNCE
Graph augmentations
Lecture 15: Knowledge Graph Embeddings
TransE and RotatE
Relational reasoning
Knowledge graph learning
PART IV — Probabilistic and Generative Graph ML
Lecture 16: Probabilistic Graphical Models
Lecture 17: Variational Inference on Graphs
ELBO
Graph VAEs
Latent graph learning
Lecture 18: Generative Graph Models
PART V — Deep Graph Learning
Lecture 19: Message Passing Neural Networks
Lecture 20: Spectral Foundations of GCNs
Lecture 21: Advanced GNN Architectures
Lecture 22: Expressivity and Limitations
Lecture 23: Graph Transformers
PART VI — Scalable and Trustworthy Graph ML
Lecture 24: Graph Coarsening and Pooling
Lecture 25: Robustness, Fairness, and Privacy
Lecture 26: Dynamic and Temporal Graphs
Temporal graph learning
Event-driven graphs
Dynamic message passing
PART VII — Relational AI, RL, and Foundation Models
Lecture 27: Reinforcement Learning on Graphs
Graph traversal and exploration
RL for combinatorial optimization
Multi-agent graph systems
Lecture 28: Graph Foundation Models and Agentic AI
Research Seminar Component
The seminar component forms a major part of the course.
Students will:
Indicative topics include: