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Residual Hyperbolic Graph Convolution Networks
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Proposes R-HGCN, a residual hyperbolic graph convolution network on product Lorentz manifolds with HyperDrop (multiplicative Gaussian noise) to mitigate over-smoothing in deep hyperbolic GCNs for node classification.
Problem
Over-smoothing in deep hyperbolic graph convolutional networks causes node features to become indistinguishable as depth grows, limiting HGCN performance.
Approach
Adds a hyperbolic residual connection with hyperbolic identity mapping (GCNII-style initial-residual) on the Lorentz model, uses product manifolds whose components have different random origin points, and introduces HyperDrop, which applies multiplicative Gaussian noise to Lorentz components instead of Bernoulli masking.
Key results
- On Pubmed with 8 layers, P-HGCN[2x8] with HyperDrop reaches 80.3±0.1%, versus GCNII's 79.9±0.3% and HGCN's 80.3±0.3% baseline in the main comparison table.
- On Cora, P-HGCN[2x8] with HyperDrop improves over no-dropout by 1.7, 0.7, 0.3 and 0.2 points at 4, 8, 16 and 32 layers.
- Using HyperDrop together with DropConnect on Cora reaches 83.5±0.9%, matching GCNII at 8 layers and exceeding LGCN's 83.3%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add HyperDrop (ablation) | R-HGCN [16 × 1] (8 layers) · Pubmed | accuracy: 79.4±0.1 -> 79.9±0.2 | Helped |
| add HyperDrop (ablation) | R-HGCN [16 × 1] (8 layers) · Citeseer | accuracy: 71.9±0.3 -> 72.5±0.5 | Helped |
| add HyperDrop (ablation) | R-HGCN [16 × 1] (8 layers) · Cora | accuracy: 80.4±0.4 -> 82.5±0.4 | Helped |
| add HyperDrop (ablation) | R-HGCN [2 × 8] (8 layers) · Pubmed and Cora | accuracy: 80.0±0.1 -> 80.3±0.1; 81.5±0.2 -> 82.2±0.4 | Helped |
| add HyperDrop (ablation) | R-HGCN [2 × 8] (8 layers) · Citeseer | accuracy: 72.1±0.2 -> 72.3±0.3 | Helped |
| add DropConnect without HyperDrop (ablation) | R-HGCN · Citeseer | accuracy: 71.9±0.3 -> 71.9±0.3 | No clear effect |
| add HyperDrop (ablation) | R-HGCN · Pubmed, Citeseer, and Cora | accuracy: 79.4±0.1 -> 79.9±0.2; 71.9±0.3 -> 72.5±0.5; 80.3±0.4 -> 82.5±0.4 | Helped |
| add both HyperDrop and DropConnect (ablation) | R-HGCN · Citeseer and Cora | accuracy: 72.5±0.5 -> 72.7±0.5; 82.5±0.4 -> 83.5±0.9 | Helped |
| add hyperbolic residual connection (ablation) | R-HGCN [2 × 8], 8 layers · Pubmed | accuracy: 78.6±0.2 -> 80.3±0.0 | Helped |
| add hyperbolic residual connection (ablation) | R-HGCN [2 × 8], 16 layers · Pubmed | accuracy: 29.8±11.1 -> 79.2±0.3 | Helped |
| add hyperbolic residual connection (ablation) | R-HGCN [4 × 4], 16 layers · Pubmed | accuracy: 60.1±7.8 -> 80.0±0.2 | Helped |
| add hyperbolic residual connection (ablation) | R-HGCN [8 × 2], 16 layers · Pubmed | accuracy: 60.1±7.8 -> 80.1±0.3 | Helped |
Surprising findings
- Without the hyperbolic residual connection, 16-layer P-HGCN[2x8] accuracy collapses to 29.8±11.1% on Pubmed, showing severe degradation in deep models.
- DropConnect was reported to not improve Citeseer, whereas HyperDrop improved all three datasets.
Limitations
- Gains from HyperDrop are small (often under 1 point) and differences are within reported standard deviations in several cases.
- Evaluation limited to semi-supervised node classification on four citation/airport graphs; the hyperbolic advantage over Euclidean GCNII is not cleanly separated from tuning.
- Theoretical Dirichlet-energy argument relies on approximations (e.g., negligible coefficients) and the main proofs are deferred to supplementary material.
Experimental setup
Datasets: Pubmed Citeseer Cora Airport
Benchmarks: Pubmed Citeseer Cora Airport
Metrics: mean accuracy (%) standard deviation
Baselines: GCNII GCN GAT GraphSage SGC APPNP HGCN H2HGCN kappaGCN LGCN DropConnect
Builds on: GCNII HGCN DropConnect Dirichlet energy analysis of over-smoothing
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