Integrated Multi‑Relation Graph Neural Network (EMR‑GNN)

The presentation introduces a unified perspective on Graph Neural Networks (GNNs), showing how existing GNN propagation schemes can be derived from a common optimization objective that balances feature fitting and graph smoothness.

Based on this view, the authors propose an integrated multi‑relation GNN (EMR‑GNN). The model incorporates a regularization term that captures relation‑specific smoothness using learnable coefficients μ_r , and a fitting term that preserves original node features, forming a compact objective function.

By alternating optimization of node embeddings Z and relation coefficients μ_r , a closed‑form message‑passing rule is derived. This rule can be implemented as an iterative process that avoids over‑smoothing and over‑parameterization, requiring only a few scalar parameters per relation.

EMR‑GNN integrates the message‑passing layer with standard MLPs for feature extraction and classification, keeping the overall parameter count lower than traditional relational GNNs such as RGCN and CompGCN.

Extensive experiments on node classification benchmarks show that EMR‑GNN achieves state‑of‑the‑art accuracy with fewer parameters, remains stable when depth increases to 64 layers, and performs well on small‑scale datasets.

The authors also analyze the learned relation coefficients, confirming that they reflect the importance of each relation, and provide visualizations of node embeddings that exhibit clear class separation.

Finally, a Q&A section addresses differences from attention mechanisms, scalability to large graphs, incorporation of edge features, and the trend toward mathematically grounded GNN design.