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HyperDefender: A Robust Framework for Hyperbolic GNNs

AAAI 2025 · Graph learning › GNN architectures · approach: Robustness, privacy, and fairness of GNNs · 3 citations (OpenAlex)

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Proposes HyperDefender, a two-stage framework that turns hyperbolic (HyLa) embeddings into Euclidean features and applies Euclidean graph defenses (e.g., Pro-GNN-style structure learning) to make hyperbolic GNNs robust to poisoning and random perturbations.

Problem

Hyperbolic GNNs are vulnerable to adversarial attacks and noise on hierarchical graphs, and existing Euclidean defenses do not handle hierarchical structure well, so robustness of Hy-GNNs is largely unexplored.

Approach

Learn HyLa random Laplacian features from hyperbolic embeddings and feed them with a learned clean adjacency into any Euclidean defense; Pro-HyLa jointly learns a denoised adjacency (sparsity, low-rank, feature smoothness regularizers) and an SGC-based hyperbolic model.

Key results

• On Airport at 10% RND perturbation, Pro-HyLa reaches 93.25% accuracy versus 68.89% for Pro-GNN and 60.30% for NoisyGNN.
• At 25% Mettack perturbation on Cora, the method surpasses HyLa-SGC and Pro-GNN by over 58% and 6% respectively (as reported in text).
• Pro-HyLa gives the lowest average hyperbolicity deviation on Airport, Disease and Cora under most attacks in Table 3, indicating partial restoration of hierarchy.

Measured effects reported in the paper

Surprising findings

• Hy-GNNs such as HyLa-SGC are not inherently robust, and Euclidean defenses fail to handle hierarchical graphs well.
• Adversarial attacks measurably increase the Gromov delta-hyperbolicity of hierarchical graphs, degrading the hierarchy.

Limitations

• Gains are small or absent on Cora, a dataset with low hierarchy, where performance is comparable to Euclidean defenses.
• Evaluated only on three small datasets and a limited set of attacks (Mettack, random, RND).
• Hyperbolic optimization makes defense design difficult, as the paper notes; no theoretical guarantees are given.

Experimental setup

Datasets: Cora Disease Airport

Benchmarks: Cora Disease Airport

Metrics: node classification accuracy Gromov delta-hyperbolicity (Delta avg)

Baselines: Pro-GNN GNNGuard RWL-GNN GCN-Jaccard NoisyGNN HANG HyLa-SGC

Builds on: HyLa (Random Laplacian Features) Pro-GNN SGC HGCN GNNGuard

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