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Stable Fair Graph Representation Learning with Lipschitz Constraint
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Proposes SFG, a stable fair GNN that bounds the Lipschitz constant of the mask generator plus GraphSAGE encoder via a non-separable spectral bound enforced by block-coordinate projected subgradient steps, and adds chi-squared DRO over generated fair views.
Problem
Adversarial-mask-based group fair graph learning suffers from training instability (fluctuating accuracy near convergence) due to mask uncertainty and the fairness-utility trade-off.
Approach
Derives a non-separable, tight upper Lipschitz bound covering both the mask generator and GNN encoder using graph spectral theory, enforces it with a layerwise block-coordinate projected subgradient (DFB) method, and trains with chi-squared-divergence distributionally robust optimization over generated fair views.
Key results
- On Bail, SFG reaches 89.49% accuracy and 93.98% AUC versus FairVGNN's 89.24% and 91.99%, with lower EO (1.11 vs 2.49).
- On Credit, SFG achieves 80.34% accuracy and 5.44 DP vs FairVGNN 80.13% accuracy and 5.74 DP.
- SFG w/o ct (no Lipschitz constraint) is as unstable as the original FairVGNN in training accuracy curves on German.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| remove Lipschitz bound constraint (ablation) | SFG · German | Acc: 69.76 ± 0.32 -> 70.32 ± 0.46 | Hurt |
| remove DRO objective (ablation) | SFG · German | Acc: 70.24 ± 0.32 -> 70.32 ± 0.46 | Hurt |
| remove Lipschitz bound constraint (ablation) | SFG · Bail | Acc: 88.76 ± 0.76 -> 89.49 ± 1.74 | Hurt |
| remove DRO objective (ablation) | SFG · Bail | Acc: 89.06 ± 1.20 -> 89.49 ± 1.74 | Hurt |
| remove Lipschitz bound constraint (ablation) | SFG · Credit | Acc: 80.37 ± 0.05 -> 80.34 ± 0.11 | No clear effect |
| remove DRO objective (ablation) | SFG · Credit | Acc: 80.20 ± 0.23 -> 80.34 ± 0.11 | Hurt |
| add Lipschitz bound constraint and DRO objective (ablation) | SFG · German | ∆EO: 2.96 ± 2.53 -> 0.54 ± 0.74 | Helped |
| add Lipschitz bound constraint and DRO objective (ablation) | SFG · Bail | ∆EO: 1.50 ± 0.98 -> 1.11 ± 0.43 | Helped |
| add Lipschitz bound constraint and DRO objective (ablation) | SFG · Credit | ∆EO: 3.81 ± 0.65 -> 2.71 ± 0.58 | Helped |
| use a smaller Lipschitz bound τ (ablation) | SFG · Credit | training accuracy stability | Hurt |
| add DRO objective with Lipschitz bound constraint (ablation) | SFG · German | training accuracy stability | Helped |
| use DRO objective (ablation) | SFG · Bail | training accuracy stability | Helped |
Surprising findings
- Removing the DRO module alone while keeping the Lipschitz constraint gives mixed results; the DRO module only improves accuracy when combined with the Lipschitz constraint.
- FairSAD achieves zero DP and EO on German, outperforming SFG on fairness there, though SFG has better accuracy on Bail and Credit.
Limitations
- Evaluated only on three small-to-medium real-world datasets with a 2-layer GraphSAGE encoder.
- Uniform weighting of generated views is chosen for simplicity rather than optimized.
- Lipschitz threshold tau must be set manually and affects the stability-performance trade-off.
Experimental setup
Datasets: German Bail Credit
Benchmarks: German Bail Credit
Metrics: accuracy AUC-ROC delta DP delta EO training accuracy stability (rolling std)
Baselines: GCN NIFTY FairGNN FairVGNN FairSAD
Builds on: FairVGNN GraphSAGE chi-squared distributionally robust optimization accelerated iterative dual forward-backward algorithm
Closest papers by meaning
- Chasing Fairness in Graphs: A GNN Architecture Perspective (AAAI 2024 · similarity 0.88)
- DANCE: Dual Unbiased Expansion with Group-acquired Alignment for Out-of-distribution Graph Fairness Learning (ICML 2025 · similarity 0.88)
- Fair Graph U-Net: A Fair Graph Learning Framework Integrating Group and Individual Awareness (AAAI 2025 · similarity 0.87)
- Adversarial Attacks on Fairness of Graph Neural Networks (ICLR 2024 · similarity 0.86)
- FairSIN: Achieving Fairness in Graph Neural Networks through Sensitive Information Neutralization (AAAI 2024 · similarity 0.86)
- Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference (NeurIPS 2025 · similarity 0.86)
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