Research map / Graph learning / GNN architectures
Cooperative Graph Neural Networks
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Proposes Co-GNNs, where each node acts as a player choosing to listen, broadcast, both, or isolate, enabling dynamic, asynchronous, directed message passing learned via straight-through Gumbel-softmax.
Problem
Standard message passing in GNNs is static, synchronous and task-agnostic, which limits information flow for long-range dependencies, over-smoothing, heterophily, and expressiveness.
Approach
Each node chooses per layer one of four actions (Standard, Listen, Broadcast, Isolate) via a learned action network, inducing a dynamic directed computation graph; an environment network then performs the message passing on that graph. Actions are sampled with straight-through Gumbel-softmax so the two networks train jointly.
Key results
- On RootNeighbors, Co-GNN(Σ,μ) reaches MAE 0.079, versus 0.329 for MeanGNN and 0.442 for GAT.
- On heterophilic node classification, Co-GNN(Σ,Σ) reaches 91.57% on roman-empire and Co-GNN(μ,μ) reaches 97.31% ROC AUC on minesweeper, claimed state-of-the-art across the board.
- Co-GNNs report an average 2.23% accuracy improvement over all baselines across the heterophilic datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Co-GNN(Σ,μ) instead of the strongest reported RootNeighbors baseline | RootNeighbors regression · RootNeighbors | MAE: 0.329 -> 0.079 | Helped |
| Use a sum-aggregation action network instead of a mean-aggregation action network (ablation) | Co-GNN on RootNeighbors · RootNeighbors | MAE: 0.339 -> 0.079 | Helped |
| Use a mean-aggregation environment network instead of a sum-aggregation environment network (ablation) | Co-GNN(Σ,*) on RootNeighbors · RootNeighbors | MAE: 0.196 -> 0.079 | Helped |
| Use a sum-aggregation action network rather than GAT, GCN, or MeanGNN as the action network (ablation) | Co-GNN on RootNeighbors · RootNeighbors | MAE | Helped |
| Use MeanGNN or GAT rather than GCN as the environment network (ablation) | Co-GNN on Minesweeper · Minesweeper | ROC AUC | Helped |
| Replace SumGNN with Co-GNN(Σ,Σ) | Graph classification · NCI1 | accuracy: 80.0 -> 80.6 | Helped |
| Replace the base GIN architecture with Co-GNN(ε,ε) | LRGB · Peptides-func | mean average precision | Helped |
| Use Co-GNN(*,*) rather than GCN | LRGB · Peptides-func | mean average precision: 0.6860 -> 0.6990 | Helped |
| Use Co-GNN with learned actions rather than classical MPNNs | Heterophilic node classification · roman-empire and minesweeper | accuracy and ROC AUC: +3.19% accuracy; +3.62% ROC AUC | Helped |
| Use Co-GNN(Σ,Σ) rather than SumGNN | Cycles graph classification · Cycles | accuracy: 50 % -> 100% | Helped |
| Use Co-GNN(μ,μ) rather than MeanGNN | Cycles graph classification · Cycles | accuracy: 50 % -> 100% | Helped |
| Use Co-GNN(ε,ε) rather than GIN | LRGB · Peptides-func | mean average precision | Helped |
Surprising findings
- On cora the learned action network gradually isolates nodes in deeper layers (all edges dropped at layer 9), while on roman-empire the fraction of kept edges rises to 99% in deep layers.
- Co-GNN(μ,μ) performs comparably to plain MeanGNN on RootNeighbors, suggesting the action network adds little when it cannot count degrees.
Limitations
- Training is volatile and sensitive to hyperparameters because sampling of actions introduces variance.
- Expressive power gain relies on sampling randomness, which is unstable; the model is not designed for expressiveness.
- Optimization becomes increasingly difficult as the number of layers grows.
Experimental setup
Datasets: RootNeighbors roman-empire amazon-ratings minesweeper tolokers questions Cycles Peptides-func IMDB-B IMDB-M REDDIT-B REDDIT-M
Benchmarks: RootNeighbors roman-empire amazon-ratings minesweeper tolokers questions Peptides-func TUDataset graph classification pubmed cora
Metrics: MAE accuracy ROC AUC average precision
Baselines: GCN GraphSAGE GAT GT GCNII DRew CRaWl GIN DGCNN DiffPool SumGNN MeanGNN
Builds on: message passing neural networks Gumbel-softmax GCN GIN GAT
Closest papers by meaning
- Towards Dynamic Message Passing on Graphs (NeurIPS 2024 · similarity 0.89)
- Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective (ICLR 2025 · similarity 0.87)
- Bundle Neural Network for message diffusion on graphs (ICLR 2025 · similarity 0.87)
- Learning on Large Graphs using Intersecting Communities (NeurIPS 2024 · similarity 0.87)
- Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks (NeurIPS 2024 · similarity 0.87)
- AutoSGNN: Automatic Propagation Mechanism Discovery for Spectral Graph Neural Networks (AAAI 2025 · similarity 0.87)
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