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Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks
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Proposes SSMA, a plug-and-play MPGNN aggregator that treats neighbor features as 2D discrete signals and sequentially circularly convolves them, adding neighbor-mixing ability over sum aggregation.
Problem
Sum-based aggregators in message passing GNNs separate multisets in theory but perform worse in practice, which the authors attribute to their inability to mix features across distinct neighbors.
Approach
Formalize a "neighbor-mixing" measure (mixed second derivatives across neighbors), show sum aggregators have zero cross-neighbor mixing, and propose SSMA: a generalized DeepSets polynomial encoding of vector features whose coefficients are computed by sequential 2D circular convolution (via FFT), with geometric-mean normalization, low-rank compressor, and attention-based neighbor slot selection fo
Key results
- On TU datasets with 10-fold CV, GIN + SSMA improves IMDB-B accuracy from 71.3 to 74.1 and ZINC MAE from 0.252 to 0.222 (GIN baseline).
- ESAN + SSMA reaches 96.32% on MUTAG and 80.6% on IMDB-B, versus 91.1% and 77.1% for ESAN.
- Reported average improvements over sum baselines of 8.9% on OGB-Arxiv, 23.86% on OGB-Products, and 13.4% on molpcba.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace sum aggregation with SSMA in ESAN | ESAN · PTC-MR | accuracy: 69.2 -> 77.89 | Helped |
| Replace sum aggregation with SSMA in ESAN | ESAN · MUTAG | accuracy: 91.1 -> 96.32 | Helped |
| Replace sum aggregation with SSMA in ESAN | ESAN · PROTEINS | accuracy: 75.9 -> 80.69 | Helped |
| Replace sum aggregation with SSMA in ESAN | ESAN · IMDB-B | accuracy: 77.1 -> 80.6 | Helped |
| Replace sum aggregation with SSMA in ESAN | ESAN · ZINC | MAE: 0.102 -> 0.096 | Helped |
| Replace sum aggregation with SSMA in GAT | GAT · Peptides-f | AP: 63.4 -> 63.6 | Helped |
| Replace sum aggregation with SSMA in GCN | GCN · Peptides-s | MAE: 0.28 -> 0.26 | Helped |
| Replace sum aggregation with SSMA in GraphGPS | GraphGPS · Arxiv | accuracy: 63.87 -> 66.71 | Helped |
| Replace sum aggregation with SSMA in GCN | GCN · Products | accuracy: 63.8 -> 72.3 | Helped |
| Replace sum aggregation with SSMA in ESAN | ESAN · molhiv | AUROC: 0.76 -> 0.83 | Helped |
| Replace sum aggregation with SSMA in GCN | GCN · molpcba | AP: 0.21 -> 0.23 | Helped |
Surprising findings
- Sum-based aggregators fail even on the simple SumOfGram task, even with analytic activations that theory says suffice for separation.
- SSMA outperforms sum aggregation despite using a smaller hidden dimension under the same parameter budget.
Limitations
- Representation size scales quadratically with the number of neighbors, O(n^2 d).
- Convolution (product over neighbors) is numerically unstable, requiring explicit normalization.
- Dense neighborhoods require neighbor selection (random or attention slots) to remain tractable.
Experimental setup
Datasets: ENZYMES PTC-MR MUTAG PROTEINS IMDB-B ZINC ogbg-molhiv ogbg-molpcba ogbn-arxiv ogbn-products peptides-func peptides-struct
Benchmarks: TU datasets (ENZYMES, PTC-MR, MUTAG, PROTEINS, IMDB-B) ZINC OGB LRGB
Metrics: accuracy MAE ROC-AUC AP
Baselines: GCN GAT GATv2 GIN GraphGPS PNA ESAN sum aggregation
Builds on: DeepSets GAT PNA GraphGPS ESAN
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