01
Foundations
Message passing, its theory and its encoders
1IntroductionWhy so much of the world's data is a graph, why ordinary deep learning chokes on it, and the three kinds of questions we ask of graphs.
2Node EmbeddingsTurn every node into a vector so that "close in the graph" becomes "close in space" — learned from random walks instead of hand-made features.
3Graph Neural NetworksReplace the embedding lookup table with a neural network that lets every node repeatedly gather and transform messages from its neighbours.
4A General Perspective on GNNsEvery GNN is a few choices in a five-part design space; GCN, GraphSAGE and GAT are just three points in it — and depth is not free.
5GNN Augmentation & TrainingThe input graph is rarely the best computation graph, and a graph dataset can't be split like a pile of images — here is the full training pipeline done right.
6Theory of GNNsA message-passing GNN can only tell apart what its neighbourhood aggregation can tell apart; sum aggregation (GIN) reaches the ceiling, and that ceiling is the Weisfeiler–Lehman test.
7Designing Powerful Graph EncodersMessage passing is stuck at the 1-WL ceiling because constant inputs inherit the graph's symmetries; inject structure (closed loops, eigenvectors, cycle counts) or position (anchor distances) and the ceiling breaks.
8Graph TransformersSelf-attention is message passing on a complete graph — so a graph transformer is a transformer that is told about the real graph through its tokens, its positional encodings and its attention scores.
02
Typed and relational data
Heterogeneous graphs, knowledge graphs, recommenders, databases
9Heterogeneous GraphsWhen nodes and edges come in different types, give each relation type its own message function — and then fight the parameter explosion that follows.
10Knowledge GraphsComplete a knowledge graph by embedding entities and relations so that a relation acts as a geometric operation — translation, projection, scaling or rotation — and pick the geometry that matches the logic of your relations.
11GNNs for Recommender SystemsRecommendation is link prediction on a user–item bipartite graph; the best models diffuse embeddings along that graph and train them with a personalised ranking loss.
12Relational Deep LearningMost of the world's valuable data sits in relational databases; treat every row as a node and every foreign key as an edge, and a temporal GNN learns the features that data scientists spend months hand-engineering.
13Advanced Architectures in RDLRelational entity graphs have a shape of their own — junction tables, bridges, hubs, timestamps — so the best RDL models rewire message passing along "atomic routes" (RelGNN) or tokenise rich context for a transformer (RelGT).
03
Generality and language models
Foundation models, LLMs and agents on graphs
14Advanced Topics in GNNsCan one pretrained graph model solve a new task on a new graph from a few examples, with no gradient updates? PRODIGY does it with "prompt graphs"; the Relational Transformer does it for any database by tokenising cells.
15Foundation Models for KGsTo transfer across knowledge graphs with different entities and different relations, stop learning a vector per relation — derive relation embeddings from how relations interact, with a model that is equivariant to renaming both nodes and relations.
16LLMs + GNNsLLMs are fluent but shaky at multi-hop, precise reasoning over structured facts; GNNs are small, deterministic and multi-hop by construction — so let the GNN feed the LLM (GraphRAG, G-Retriever) or the LLM feed the GNN (text-attributed graphs, GLEM).
17Agents + GraphsFrom pretraining to RLHF, then two problems agents still fail at — using tools to navigate semi-structured knowledge graphs (STaRK, AvaTaR) and actually collaborating with humans over many turns (CollabLLM).
04
Generation and design
Generative models and the design space
18Deep Generative Models for GraphsTurn a graph into a sequence of "add node, add edges" decisions, learn it with an autoregressive model (GraphRNN), and steer generation toward goals like drug-likeness with a GNN policy trained by reinforcement learning (GCPN).
19ConclusionInstead of asking "which GNN is best?", map the whole space of GNN designs and of tasks — then transfer the best design from the most similar known task (GraphGym) — and look back at the full course.
05
Bonus pages
From the lecture notes: topics the slides skip
20Bonus A: Classic Graph ML and ScalingBefore GNNs, people described nodes, links and whole graphs with hand-made features (degree, centrality, graphlets, Katz, WL colours). Then two simple ideas — spread labels along edges (label propagation, Correct & Smooth) and shrink the graph you compute on (neighbour sampling, Cluster-GCN, Simplified GCN) — turned out to compete with deep GNNs on real, huge graphs.
21Bonus B: Geometry, Subgraphs and TrustThree ideas the 2024 notes add beyond this year's slides: GNNs that respect the symmetry of 3D space (rotate a molecule and its energy must not change), subgraphs and motifs as the building blocks of networks (found fast with order embeddings), and explanations that say which edges and features made a GNN decide (GNNExplainer, fidelity).
06
How to use these pages
Read in orderEach page opens with "In short" and a picture, then the concept sections. The slide-by-slide walkthrough is collapsed: open it when you want the lecture verbatim. Tick "got it" per section; the roadmap and this index remember your progress.
Predict, then reveal"Check yourself" answers stay hidden until you ask, and every page has a proof workshop with graded hints. Commit to an answer first: being wrong and then corrected is how it sticks.
Review across sessionsThe cumulative review mixes questions, flashcards and proof problems from every session you have reached, with spaced repetition so missed items come back sooner.
Play with the figuresEvery interactive figure has sliders or buttons. They run in the browser with no server; the numbers in the notebook-based ones are measured results from
notebooks/cs224w/.Then open the notebookEvery Lab section links its marimo notebook. Run
uv run marimo edit notebooks/cs224w from the repository root.Frontier and SNA bridgeWritten for a reader who knows classical social network analysis: what each lecture inherits from it, what it changes, and what the 2025–26 conferences did to the lecture's claims. Each bridge links to the units of the SNA course that teach the classic side in full.