FUGNN: Harmonizing Fairness and Utility in Graph Neural Networks

TL;DR

This work tackles the fairness–utility trade-off in graph neural networks by introducing FUGNN, a spectral learning framework that truncates the graph spectrum to principal eigenvectors and uses a transformer-based module to optimize eigenvector distribution. Theoretical analysis shows that deep representations are dominated by the eigenvector associated with the largest magnitude eigenvalue, justifying spectrum truncation for fairness without sacrificing utility, and that non-principal components decay exponentially with depth. The method combines Fairness-aware Eigenvalue Selection via Arnoldi with Optimization of Eigenvectors Distribution to produce a spectrum that reduces sensitive-feature leakage while maintaining predictive accuracy, yielding superior or competitive results on six real-world datasets. Empirical results demonstrate improved fairness metrics (lower $\Delta_{SP}$ and $\Delta_{EO}$) and strong utility, alongside scalable training costs due to $O(nK^2)$ eigendecomposition, highlighting the practical viability of spectrum-based fairness in GNNs.

Abstract

Fairness-aware Graph Neural Networks (GNNs) often face a challenging trade-off, where prioritizing fairness may require compromising utility. In this work, we re-examine fairness through the lens of spectral graph theory, aiming to reconcile fairness and utility within the framework of spectral graph learning. We explore the correlation between sensitive features and spectrum in GNNs, using theoretical analysis to delineate the similarity between original sensitive features and those after convolution under different spectra. Our analysis reveals a reduction in the impact of similarity when the eigenvectors associated with the largest magnitude eigenvalue exhibit directional similarity. Based on these theoretical insights, we propose FUGNN, a novel spectral graph learning approach that harmonizes the conflict between fairness and utility. FUGNN ensures algorithmic fairness and utility by truncating the spectrum and optimizing eigenvector distribution during the encoding process. The fairness-aware eigenvector selection reduces the impact of convolution on sensitive features while concurrently minimizing the sacrifice of utility. FUGNN further optimizes the distribution of eigenvectors through a transformer architecture. By incorporating the optimized spectrum into the graph convolution network, FUGNN effectively learns node representations. Experiments on six real-world datasets demonstrate the superiority of FUGNN over baseline methods. The codes are available at https://github.com/yushuowiki/FUGNN.

Figures (4)

• Figure 1: The sacrificed utility of fairness-aware GNNs. The utility is measured by the prediction accuracy and the fairness is measured by the -$\Delta_\text{SP}$.
• Figure 2: The framework of FUGNN. The model applies spectral truncation via eigenvalue selection and eigenvector distribution optimization with fairness considerations. The top and bottom illustrate the two stages from the perspective of feature-level representations and feature channels, respectively.
• Figure 3: The accuracy and $\Delta_\text{SP}$ trade-off. Upper-left corner is preferable.
• Figure 4: The accuracy and $\Delta_\text{EO}$ trade-off. Upper-left corner is preferable.