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Discrete Curvature Graph Information Bottleneck
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Proposes CurvGIB, which learns task-relevant Ollivier-Ricci curvature via a variational information bottleneck objective combined with Ricci flow-style structure refinement and bi-level optimization for node classification on GNNs.
Problem
GNN message passing depends on efficient information transport, but existing curvature-based rewiring uses heuristic topology priors and is not tied to downstream tasks; graph structure learning is costly and not task-aligned.
Approach
Learns the Ricci curvature itself under a variational information bottleneck objective, using a Laplacian-based differentiable approximation of Ollivier-Ricci curvature (inspired by DeepRicci) and a Ricci-flow-style edge weight update, then samples refined structures via a Bernoulli relaxation, optimized bi-level.
Key results
- CurvGIB reports the best ACC on all seven node-classification datasets in the table, e.g., 89.0% on Cora and 93.7% on Amazon-Computers.
- On Cora, CurvGIB reaches 84.3 macro-F1 versus 62.7 for BORF (the strongest curvature baseline in the table).
- Under random 10-50% edge removal/addition on Cora, CurvGIB's accuracy stays relatively stable while GCN drops about 10% with 50% missing edges.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CurvGIB instead of the strongest baseline | node classification · Cora | accuracy: 87.5±0.2 -> 89.0±0.9 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Cora | Macro-F1: 82.2±8.1 -> 84.3±0.9 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Citeseer | accuracy: 73.8±0.2 -> 75.5±0.1 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Citeseer | Macro-F1: 84.7±8.5 -> 73.5±1.4 | Hurt |
| Use CurvGIB instead of the strongest baseline | node classification · PubMed | accuracy: 86.9±4.7 -> 88.0±0.1 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · PubMed | Macro-F1: 86.1±5.5 -> 78.9±0.9 | Hurt |
| Use CurvGIB instead of the strongest baseline | node classification · CS | accuracy: 92.9±0.3 -> 94.2±0.5 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · CS | Macro-F1: 87.4±1.7 -> 91.2±0.5 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Physics | accuracy: 95.0±4.8 -> 96.5±0.3 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Physics | Macro-F1: 91.9±0.5 -> 87.7±0.5 | Hurt |
| Use CurvGIB instead of the strongest baseline | node classification · Amazon-C | accuracy: 86.5±0.7 -> 91.9±1.4 | Helped |
| Use CurvGIB instead of the strongest baseline | node classification · Amazon-C | Macro-F1: 84.2±7.3 -> 83.9±1.7 | Hurt |
Surprising findings
- Graph structure learning baselines (SUBLIME, MVPOOL-SL) sometimes hurt performance on Amazon datasets relative to GCN.
Limitations
- Only evaluated on node-level tasks; graph-level extension left to future work.
- Reported results use 10-fold cross-validation with high standard deviations for some baselines; the complexity analysis claims O(n^2) under d << n assumption.
Experimental setup
Datasets: Cora CiteSeer PubMed Coauthor CS Coauthor Physics Amazon-Computers Amazon-Photos
Benchmarks: Cora CiteSeer PubMed CS Physics Amazon-C Amazon-P
Metrics: accuracy macro-F1
Baselines: GCN GAT GIN GraphSAGE SDRF BORF CurvGN SUBLIME MVPOOL-SL RGIB
Builds on: Variational Information Bottleneck DeepRicci GIB BORF SDRF
Closest papers by meaning
- The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisited (ICLR 2025 · similarity 0.89)
- Effective Structural Encodings via Local Curvature Profiles (ICLR 2024 · similarity 0.88)
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025 · similarity 0.87)
- Spectro-Riemannian Graph Neural Networks (ICLR 2025 · similarity 0.87)
- Bundle Neural Network for message diffusion on graphs (ICLR 2025 · similarity 0.85)
- What do Graph Neural Networks learn? Insights from Tropical Geometry (NeurIPS 2024 · similarity 0.85)
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