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Graph Adaptive Autoregressive Moving Average Models
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Proposes GRAMA, a permutation-equivariant graph sequence model that stacks graph copies into a sequence and applies a learnable, selectively-attended ARMA recurrence on top of GNN backbones (GCN, GatedGCN, GPS).
Problem
Graph SSMs either break permutation equivariance (node ordering, random walks) or only model pairwise/short sequences, limiting long-range propagation and mitigation of oversquashing in GNNs.
Approach
Transform a static graph into a sequence of L node-feature copies and apply a graph-adaptive neural ARMA recurrence whose AR and MA coefficients are predicted by attention over the state and residual sequences, with a GNN backbone supplying the residual; the block is shown to be equivalent to a linear SSM.
Key results
- On Peptides-func, GRAMA-GCN reaches 70.93 AP vs 67.51 for SWAN and 67.39 for Graph-Mamba (best reported).
- On Peptides-struct, GRAMA-GPS achieves 0.2436 MAE, improving over SWAN (0.2485) and the GraphGPS+LapPE baseline (0.2500).
- On graph property prediction, GRAMA-GPS obtains the best log10(MSE) on Diameter (-0.8663) and Eccentricity (-1.3012) versus SWAN (-0.5981 and -0.0739).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add GRAMA to GPS | GPS · Graph property prediction: Diameter | log10(MSE): -0.5121±0.0426 -> -0.8663±0.0514 | Helped |
| Add GRAMA to GPS | GPS · Graph property prediction: SSSP | log10(MSE): -3.5990±0.1949 -> -3.9349±0.0699 | Helped |
| Add GRAMA to GPS | GPS · Graph property prediction: Eccentricity | log10(MSE): 0.6077±0.0282 -> -1.3012±0.1258 | Helped |
| Add GRAMA to GCN | GCN · Peptides-func | AP: GCN: 59.30±0.23; GRAMAGCN: 70.93±0.78 | Helped |
| Add GRAMA to GCN | GCN · Peptides-struct | MAE: GCN: 0.3496±0.0013; GRAMAGCN: 0.2439±0.0017 | Helped |
Surprising findings
- Plain GCN augmented with GRAMA outperforms GPS-based variants on SSSP and Peptides-func, suggesting the ARMA module contributes much of the gain.
Limitations
- Sequence length L and number of blocks S are hyperparameters, adding overhead relative to the backbone.
- Theoretical oversquashing claims are supported by synthetic tasks and stability analysis rather than full end-to-end guarantees.
Experimental setup
Datasets: Peptides-func Peptides-struct ZINC-12k OGBG-MOLHIV Cora CiteSeer Pubmed MNIST CIFAR10 PATTERN CLUSTER MalNet-Tiny
Benchmarks: Peptides-func Peptides-struct graph feature transfer graph property prediction (Diameter, SSSP, Eccentricity) ZINC-12k OGBG-MOLHIV Cora CiteSeer Pubmed MNIST CIFAR10 PATTERN
Metrics: mean squared error log10(MSE) AP MAE
Baselines: GCN GAT GraphSAGE GIN GCNII ARMA GraphCON A-DGN SWAN GPS Graph-Mamba GMN
Builds on: Graph ARMA Mamba S4 GraphGPS
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