Principal Neighbourhood Aggregation (PNA)

Most GNN layers pick a single aggregation function and hope it fits every neighborhood. PNA argues this is provably insufficient for continuous features: a single aggregator cannot distinguish distributions that differ only in statistics it does not compute. The paper extends the WL-style expressiveness framework to continuous features, shows multiple complementary aggregators are needed, and builds the layer to match: mean, max, min and standard deviation aggregations, each modulated by degree-based scalers (identity, amplification, attenuation) that let the network react to neighborhood size. A logarithmic moment normalization keeps the combination numerically stable.\n\nThe NeurIPS 2020 paper introduces a synthetic multi-task benchmark designed to isolate aggregation quality, where PNA scores -3.13 log-MSE against -1.99 for the best single-aggregator GIN and -2.04 for GCN, winning even with fewer parameters than enlarged single-aggregator baselines. PNA also performs strongly on larger-graph extrapolation, where the max aggregator's robustness carries over. The multiple-aggregator principle has since become common in expressive GNN design.

Paper-reported: -3.13 log-MSE on the authors' multi-task benchmark vs -1.99 for the best single-aggregator GIN and -2.04 for GCN (Corso et al., NeurIPS 2020). Benchmark is synthetic and author-designed; treat as supporting rather than decisive evidence.