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Motif-Aware Riemannian Graph Neural Network with Generative-Contrastive Learning
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Proposes MotifRGC, a self-supervised Riemannian GCN (D-GCN) with a product manifold containing a diversified hypersphere factor and a generalized Fourier kernel layer, trained with a motif-generator vs. discriminator minmax game plus motif-aware hard contrastive learning.
Problem
Riemannian graph representation learning suffers from single-curvature manifolds, numerical instability of exponential/logarithmic maps, and lacks motif regularity modeling, all without external labels.
Approach
Builds a diverse-curvature product manifold with a diversified hypersphere factor, replaces exp/log maps with a generalized Fourier (gyrovector kernel) feature map into Euclidean GCN layers, and learns curvature via a GAN-style motif generator/discriminator while contrasting factor views with a motif-aware hardness weighting.
Key results
- Ours(GCN) reaches 97.37 AUC on Cora link prediction, versus 90.11 for GCN backbone and 95.22 for the best prior baseline Q-GCN.
- Node classification on Cora reaches 83.7% ACC for the GCN-backbone variant versus 82.6% for the best baseline LGCN.
- Removing the generalized Fourier map and using log map yields NaN on Citeseer link prediction with the GCN backbone.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use MotifRGC instead of the backbone GCN | GCN · link prediction across Cora, Citeseer, Pubmed, and Airport | AUC: +7.36% AUC gain | Helped |
| add motif-aware hardness to contrastive learning (ablation) | MotifRGC · Cora and Citeseer | AUC: 97.05 -> 97.37; 98.36 -> 98.54 | Helped |
| add Riemannian contrastive learning (ablation) | MotifRGC · Cora and Citeseer | AUC: 96.30 -> 97.37; 97.86 -> 98.54 | Helped |
| add generalized Fourier map instead of logarithmic map (ablation) | MotifRGC · Citeseer | AUC | Helped |
| add motif generation to the contrastive-only model (ablation) | MotifRGC · Cora and Citeseer | AUC: 95.02 -> 97.37; 96.80 -> 98.54 | Helped |
| increase learnable factors from three to four (ablation) | MotifRGC-GCN · Cora | AUC: 97.37 -> 97.99 | Helped |
| increase learnable factors from three to four (ablation) | MotifRGC-GAT · Cora | AUC: 98.86 -> 99.16 | Helped |
| increase learnable factors from three to four (ablation) | MotifRGC-GCN · Citeseer | AUC: 98.54 -> 99.03 | Helped |
Surprising findings
- The log-map variant produces NaN on Citeseer link prediction, illustrating numerical instability of exponential/logarithmic maps.
Limitations
- Results on only four small public datasets (Cora, Citeseer, Pubmed, Airport).
- Only triangle motifs are focused on in the generator and contrast design.
- Hardware and training cost not reported.
Experimental setup
Datasets: Cora Citeseer Pubmed Airport
Benchmarks: Cora Citeseer Pubmed Airport
Metrics: AUC AP ACC
Baselines: GCN GAT SAGE SME HGCN HGNN LGCN kappa-GCN H-to-H SelfMG Q-GCN fully H
Builds on: HGCN kappa-GCN Q-GCN InfoNCE Bochner's theorem
Closest papers by meaning
- Adaptive Riemannian Graph Neural Networks (AAAI 2026 · similarity 0.91)
- Spectro-Riemannian Graph Neural Networks (ICLR 2025 · similarity 0.89)
- Toward a Unified Geometry Understanding : Riemannian Diffusion Framework for Graph Generation and Prediction (NeurIPS 2025 · similarity 0.88)
- RMLR: Extending Multinomial Logistic Regression into General Geometries (NeurIPS 2024 · similarity 0.87)
- DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation (NeurIPS 2026 · similarity 0.86)
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025 · similarity 0.85)
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