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Do We Really Need Message Passing in Brain Network Modeling?
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Proposes Brain Quadratic Network (BQN), replacing message passing with Hadamard-product quadratic layers on Pearson-correlation brain graphs, and shows it beats GNN and graph Transformer baselines on ABIDE and ADNI with lower runtime.
Problem
Brain network classification with GNNs and graph Transformers relies on message passing, but brain networks built from pairwise Pearson correlations reuse the adjacency matrix as node features, so message passing is argued to be redundant or poorly exploited.
Approach
Replace matrix-product message passing with quadratic-network layers using Hadamard products (H_l = H_{l-1} ⊙ (A W_l)) plus a Hadamard residual; the authors show this update equals a NMF-based community detection update on the adjacency matrix.
Key results
- On ABIDE, BQN reaches 79.85 AUC and 72.53 ACC, versus 77.99 AUC and 70.10 ACC for the runner-up ALTER.
- On ADNI, BQN reaches 74.18 AUC and 68.62 ACC, versus 71.86 AUC and 66.92 ACC for ALTER.
- BQN has the lowest reported training time on both datasets (11.31 s on ABIDE, 3.33 s on ADNI for 100 epochs).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use BQN instead of ALTER | brain disorder classification · ABIDE | AUC: 77.99±2.21 -> 79.85±1.27 | Helped |
| use BQN instead of A-GCL | brain disorder classification · ABIDE | ACC: 71.04±2.40 -> 72.53±1.41 | Helped |
| use BQN instead of ALTER | brain disorder classification · ADNI | AUC: 71.86±3.13 -> 74.18±3.34 | Helped |
| use BQN instead of BrainNETTF | brain disorder classification · ADNI | ACC: 67.85±2.92 -> 68.62±3.22 | Helped |
| add the Hadamard residual term (ablation) | BQN · ABIDE | AUC | Helped |
| add the Hadamard residual term (ablation) | BQN · ABIDE | ACC | Helped |
| add the Hadamard residual term (ablation) | BQN · ABIDE | SEN | Helped |
| add the Hadamard residual term (ablation) | BQN · ADNI | AUC | Helped |
| add the Hadamard residual term (ablation) | BQN · ADNI | ACC | Helped |
| add the Hadamard residual term (ablation) | BQN · ADNI | SEN | Helped |
| increase the number of BQN layers beyond 3 (ablation) | BQN · ABIDE | AUC | Hurt |
| increase the number of BQN layers beyond 3 (ablation) | BQN · ADNI | ACC | Hurt |
Surprising findings
- A simple linear classifier on the raw connectivity matrix outperforms basic GNNs and Transformers on ABIDE and ADNI.
- Graph Transformers with brain-specific designs such as ContrastPool score below 60 AUC on ABIDE, underperforming the simpler baselines.
Limitations
- Evaluated only on two small fMRI datasets (ABIDE and ADNI) with a few hundred subjects, and performance declines with depth, attributed to overfitting.
- Baseline results were re-run under unified settings rather than taken from original papers, so comparisons depend on those choices.
Experimental setup
Datasets: ABIDE ADNI
Benchmarks: ABIDE ADNI
Metrics: AUC ACC SEN SPE running time
Baselines: GCN GAT BrainGNN BrainGB FBNETGEN A-GCL SAN Graphormer GraphTrans BrainNETTF ContrastPool ALTER
Builds on: GCN Graph Transformer quadratic neural networks (Fan et al.) BrainGB BrainNETTF
Closest papers by meaning
- Biologically Plausible Brain Graph Transformer (ICLR 2025 · similarity 0.85)
- Long-range Brain Graph Transformer (NeurIPS 2024 · similarity 0.84)
- BrainOOD: Out-of-distribution Generalizable Brain Network Analysis (ICLR 2025 · similarity 0.84)
- Towards Dynamic Message Passing on Graphs (NeurIPS 2024 · similarity 0.84)
- Accurate and Scalable Graph Neural Networks via Message Invariance (ICLR 2025 · similarity 0.83)
- Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs (ICML 2024 · similarity 0.83)
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