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This is Lecture 9 of Stanford CS224W: Machine Learning with Graphs, Fall 2025, dated 2025-10-21. It follows the course schedule and official slides; the slides credit Jure Leskovec, Charilaos Kanatsoulis, and the course team.
Materials and gaps
Public materials include the slides and optional readings listed on the schedule. Canvas video, live Q&A, board work, and Ed discussions are unavailable, so this article does not reconstruct them. The public 2021 videos are not evidence for a 2025 lecture.
Complete lecture agenda
1. Heterogeneous graph schemas
A heterogeneous graph has multiple node or edge types, such as author–paper–venue. Collapsing every relation into one adjacency matrix makes 'author writes paper' indistinguishable from 'paper appears at venue.'
2. Relation-specific messages
Message passing must account for source type, relation type, and target type. Each typed edge may receive its own transformation before the target aggregates messages across relations.
3. R-GCN
R-GCN assigns parameters to relations and controls their count through basis or block decomposition. It suits multi-relational graphs, but graphs with many relation types still require careful sharing.
4. Heterogeneous Graph Transformer
HGT introduces node and edge types into attention, messages, and updates, giving different meta-relations different projections. This changes propagation more directly than attaching one type one-hot feature.
5. Parameter sharing and scalability
Write the schema before modeling: node types, edge directions, reverse edges, available features, and prediction target. Split by time or target relation where appropriate to prevent future information leaking through another relation.
A complete heterogeneous-graph modeling agenda
The schema is the first model
Node types, edge types, directions, and feature availability define which messages can exist before a neural layer is chosen. Collapsing types may erase semantics; proliferating types may leave too little data per parameter block.
Canonical edge types
A canonical relation is a source-type, relation, destination-type triple. The same relation name between different endpoint types is not automatically the same transformation, and reverse edges must be declared rather than silently added.
The R-GCN update
R-GCN transforms neighbor states with relation-specific weights, normalizes messages, and combines them with a self transformation. This preserves relation semantics but makes normalization and parameter sharing part of the architecture.
Basis decomposition
Represent each relation matrix as a learned combination of a small set of bases. This reduces parameter growth and shares statistical strength, though too few bases can force unrelated relations into the same subspace.
HGT typed attention
HGT conditions query, key, value, and attention priors on node and relation types. The resulting weight answers which typed neighbor matters to a typed receiver, not just which adjacent node has a similar feature vector.
Time and relative time
Temporal edges require a prediction cutoff and often a relative-time encoding. Sampling or feature construction that crosses the cutoff leaks the future even if the target edge itself is removed.
Feature alignment
Different node types may begin with text, categories, dense vectors, or no features. Type-specific input encoders can align dimensions, but an ID lookup remains transductive and must not be described as cold-start support.
Heterogeneous sampling
Uniform neighbor sampling can let frequent relations dominate and rare types disappear. Per-relation fanouts or typed walks change the training distribution and must be recorded with the model.
Splits and leakage
Information may reach a test label through another relation, a reverse edge, or a future event. Split construction must remove the whole forbidden information path, not only the literal supervised edge.
Acceptance protocol
Compare a type-collapsed baseline, relation-specific model, and shared-parameter variant under the same budget. Break metrics down by relation frequency, endpoint type, degree, and seen/unseen entities, and save the schema version.
Implementation and evidence boundaries
Parameter growth
One full matrix per relation scales poorly and underserves rare relations. State basis, block, or generated-weight sharing.
Type-specific normalization
Across-relation and within-relation normalization treat high-frequency relations differently and are part of model semantics.
Cold start
Shared type encoders can handle new attributed entities; ID and relation lookup tables cannot handle unseen vocabularies directly.
Metric breakdown
Report micro and macro-per-relation results by degree, frequency, type, and seen/unseen status.
Schema versioning
Save schema hashes, type vocabularies, feature-encoder versions, and explicit behavior for unseen types.
Final schema acceptance
Trace one prediction through its typed edges, transformations, normalization, and cutoff. Then remove reverse or auxiliary relations in turn; any large change identifies a dependency that must be named in the claim and leakage audit.
Self-study checkpoint
Take one minimal graph or set of triples and write down the input, invariances retained by the model, output, and evaluation. If two examples that should differ remain identical at every step, you have located an expressive gap in the encoder.
Course video sources
Checked live: the archived Fall 2025 official page lists no public recording link (its Canvas entry is empty), and the current Fall 2026 official page says lecture videos are on Canvas for enrolled students only; the Canvas entry redirects to the Stanford sign-in page. The public Stanford Online YouTube playlists currently cover only the 2021 and 2023 offerings, whose lectures differ from the Fall 2025 offering this article follows, so they are not embedded or treated as Fall 2025 recordings.
Course and recording entries:
- Official course / lecture source
- CS224W Fall 2025 official archive
- Stanford Online CS224W public playlist (2021 offering, not Fall 2025)
- Stanford Online CS224W public playlist (2021 / 2023 offerings, not Fall 2025)
Checked: 2026-10-10.
Update Log
- 2026-10-10: Added explicit video status and checked recording sources and access notes.
- 2026-10-10: Rechecked video status. Confirmed the official pages list no public Fall 2025 recording, Canvas requires sign-in, and public playlists cover only 2021/2023; status unchanged and check date added.
References
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