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GRANOLA: Adaptive Normalization for Graph Neural Networks
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Proposes GRANOLA, a graph-adaptive normalization layer that generates per-node, per-graph affine parameters from an auxiliary MPNN fed with random node features, and reports consistent gains over standard and graph-specific normalizations on ZINC, OGB molecular, and TU datasets.
Problem
Standard normalization layers (BatchNorm, InstanceNorm, LayerNorm) were not designed for GNNs and can limit expressive power, while existing graph-specific normalizations give inconsistent benefits across tasks.
Approach
Normalize node features with affine parameters produced by an additional shallow MPNN that takes the intermediate features concatenated with random node features, making the normalization adaptive to each node of each input graph while keeping MPNN complexity and gaining RNF-level expressiveness.
Key results
- On ZINC-12k, GIN + GRANOLA reaches 0.1203 MAE versus 0.1630 for GIN + BatchNorm and 0.1574 for the best graph-specific baseline (SuperNorm).
- On ogbg-molbace, GRANOLA achieves 79.92 ROC-AUC versus 72.97 for BatchNorm, and on ogbg-molesol it reaches RMSE 0.960 versus 1.044 for GraphNorm.
- Adding GRANOLA to GSN lowers ZINC MAE from 0.1010 to 0.0766.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add RNF to the normalization GNN (ablation) | GIN + Granola · ZINC-12k | MAE: 0.1497±0.008 -> 0.1203±0.006 | Helped |
| add RNF to the normalization GNN (ablation) | GIN + Granola · molesol | RMSE: 1.088±0.032 -> 0.960±0.020 | Helped |
| add RNF to the normalization GNN (ablation) | GIN + Granola · moltox21 | ROC-AUC: 75.87±0.72 -> 77.19±0.85 | Helped |
| add RNF to the normalization GNN (ablation) | GIN + Granola · molbace | ROC-AUC: 76.23±2.06 -> 79.92±2.56 | Helped |
| add RNF to the normalization GNN (ablation) | GIN + Granola · molhiv | ROC-AUC: 77.09±1.49 -> 78.98±1.17 | Helped |
| add Granola normalization | GSN · ZINC | MAE: 0.1010±0.010 -> 0.0766±0.008 | Helped |
| add Granola normalization | GSN · molesol | RMSE: 1.003±0.037 -> 0.941±0.024 | Helped |
| add Granola normalization | GSN · moltox21 | ROC-AUC: 76.08±0.79 -> 77.84±0.63 | Helped |
| add Granola normalization | GSN · molbace | ROC-AUC: 77.40±2.92 -> 80.41±2.07 | Helped |
| add Granola normalization | GSN · molhiv | ROC-AUC: 80.39±0.90 -> 81.12±0.79 | Helped |
Surprising findings
- GRANOLA without RNF (GRANOLA-no-rnf) is theoretically no more expressive than a standard MPNN, and empirically it underperforms the full RNF version.
- Several graph-specific normalizations (e.g., GraphNorm, PairNorm) improve over BatchNorm on OGB datasets but perform worse on ZINC-12k, showing inconsistent benefits.
Limitations
- Gap remains to expressive GNNs on some datasets, suggesting the normalization GNN design could be improved.
- Memory and time remain linear in nodes but still add overhead relative to plain normalization.
- Evaluation is limited to GIN/GINE-style MPNN backbones and a set of molecular and TU datasets.
Experimental setup
Datasets: ZINC-12k ogbg-molesol ogbg-moltox21 ogbg-molbace ogbg-molhiv TUDatasets (including NCI109)
Benchmarks: ZINC-12k ogbg-molesol ogbg-moltox21 ogbg-molbace ogbg-molhiv TUDatasets (NCI109 and others)
Metrics: MAE RMSE ROC-AUC accuracy
Baselines: BatchNorm InstanceNorm LayerNorm-node LayerNorm-graph PairNorm MeanSubtractionNorm DiffGroupNorm NodeNorm GraphNorm GraphSizeNorm SuperNorm RNF-PE
Builds on: GIN Random Node Features LayerNorm GraphNorm PairNorm
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