Research map / Graph learning / GNN architectures
Improving Graph Neural Networks by Learning Continuous Edge Directions
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes CoED GNN, which learns continuous (fuzzy) edge directions via a complex-valued fuzzy Laplacian and separate in/out-neighbor aggregation, showing gains on node classification and graph-ensemble regression tasks.
Problem
Standard GNN message passing behaves like diffusion on undirected graphs, causing feature homogenization (oversmoothing) and limiting long-range information transmission and discriminative power.
Approach
Assigns each edge a learnable continuous direction (phase angle) and uses a complex-valued fuzzy graph Laplacian whose real and imaginary parts separate in- and out-neighbor messages; the phase matrix is optimized jointly with GNN weights by gradient descent.
Key results
- On node classification without edge direction learning, CoED ranks in the top three on most of 11 datasets, e.g., Roman-Empire 92.17% and SNAP-Patents 74.67% (best reported).
- On the three real graph ensemble datasets, CoED attains the lowest test loss: Perturb-seq 3.56 (vs. best baseline GAT 3.85), web traffic 5.76 (vs. GAT 6.00), power grid 2.91 (vs. DirGAT 3.28).
- On synthetic graph ensemble regression, CoED outperforms GAT, GraphGPS, MagNet, FLODE, and others and continues to improve with depth up to 10 layers while other models plateau.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CoED instead of the strongest listed baseline | Node classification models · Roman-Empire | test accuracy: 91.57\text{ $\pm$0.32} -> 92.17\text{ $\pm$0.29} | Helped |
| Use CoED instead of the strongest listed baseline | Node classification models · SNAP-Patents | test accuracy: 73.95\text{ $\pm$0.05} -> 74.67\text{ $\pm$0.02} | Helped |
| Use CoED instead of the strongest listed baseline | Node classification models · Texas | test accuracy: 85.95\text{ $\pm$5.51} -> 84.59\text{ $\pm$4.53} | Mixed |
| Use CoED instead of the strongest listed baseline | Node classification models · Squirrel | test accuracy: 44.19\text{ $\pm$2.42} -> 45.50\text{ $\pm$1.62} | Helped |
| Use CoED instead of the strongest listed baseline | Node classification models · Citeseer | test accuracy: 78.07 \text{ $\pm$1.62} -> 77.14\text{ $\pm$1.57} | Hurt |
| Learn continuous edge directions from an undirected input graph | CoED · Perturb-seq | test loss: 3.85{ $\pm$0.03} -> 3.56{ $\pm$0.03} | Helped |
| Learn continuous edge directions from an undirected input graph | CoED · Web traffic | test loss: 6.00{ $\pm$0.03} -> 5.76\text{ $\pm$0.05} | Helped |
| Learn continuous edge directions from an undirected input graph | CoED · Power grid | test loss: 3.28{ $\pm$0.17} -> 2.91\text{ $\pm$0.11} | Helped |
Surprising findings
- DirGCN performs worse than GCN on the undirected Perturb-seq graph, attributed to clashing in/out weight matrices applied to identical messages.
- Learning edge directions for standard node classification with masked test nodes would hurt performance, so the method is restricted to graph ensemble settings.
Limitations
- Learning edge directions risks overfitting in standard node classification where graph is shared between train and test nodes, so the benefit is shown mainly for graph ensemble data.
- Real Perturb-seq graph is a heuristic kNN correlation graph rather than ground truth GRN.
- Expensive hyperparameter searches; reported results rely on extensive tuning (about three weeks of training for node classification).
Experimental setup
Datasets: Roman-Empire SNAP-Patents Texas Wisconsin Arxiv-Year Squirrel Chameleon Citeseer AM-Computers AM-Photo Cora Replogle-gwps
Benchmarks: Roman-Empire SNAP-Patents Texas Wisconsin Arxiv-Year Squirrel Chameleon Citeseer AM-Computers AM-Photo Cora Replogle-gwps Perturb-seq
Metrics: test accuracy test MSE/loss
Baselines: MLP GCN SAGE GAT GGCN FLODE Sheaf MagNet Chung DirGNN Co-GNN GraphGPS
Builds on: DirGNN magnetic Laplacian GCN GAT FLODE
Closest papers by meaning
- Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily (AAAI 2026 · similarity 0.90)
- Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All? (NeurIPS 2023 · similarity 0.90)
- Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals (NeurIPS 2023 · similarity 0.89)
- What do Graph Neural Networks learn? Insights from Tropical Geometry (NeurIPS 2024 · similarity 0.89)
- Integrating Co-Training with Edge Discrimination to Enhance Graph Neural Networks Under Heterophily (AAAI 2025 · similarity 0.89)
- Edge Prompt Tuning for Graph Neural Networks (ICLR 2025 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.