Source
Xu et al. (2019), LIT-580. Read as NOTE-319. The reason is THEORY-083.
The practice
Xu et al. proposed this aggregator as GIN in LIT-580, with the proof that message passing is bounded by 1-WL and that sum followed by an MLP reaches the bound where mean and max do not. On REDDIT-BINARY and REDDIT-MULTI-5K with no node features, GIN-0 scores 92.4 and 57.5 and the mean variants sit at chance (50.0 and 20.0). On the other seven datasets GIN is best or tied, mostly within one standard deviation, and mean–MLP beats it on PTC, which is the third bullet.
- Sum, then MLP.
h_v ← MLP((1 + ε)·h_v + Σ_{u∈N(v)} h_u). Fix ε = 0 (GIN-0), which fit as well as learned ε and generalized slightly better - Read out by summing node states from every layer, and concatenate the per-layer readouts
- Know when it matters. Where the node features are weak or absent, and counts and structure are the signal, mean or max aggregation can fail outright. Where the features are informative, expect small differences, and choose by validation
Conditions
- Graph classification on small benchmarks, with 10-fold CV
- Bounded by 1-WL either way. Tasks needing cycle counts or more need positional or structural encodings