On Demographic Group Fairness Guarantees in Deep Learning

We present a theoretical framework analyzing the relationship between data distributions and fairness guarantees in equitable deep learning. We establish novel bounds that account for distribution heterogeneity across demographic groups, deriving fairness error and convergence rate bounds that characterize how distributional differences affect the fairness-accuracy trade-off. Extensive experiments across diverse modalities, including FairVision, CheXpert, HAM10000, FairFace, ACS Income, and CivilComments-WILDS, validate our theoretical findings, demonstrating that feature distribution differences across demographic groups significantly impact model fairness, with disparities particularly pronounced in racial categories. Motivated by these insights, we propose Fairness-Aware Regularization (FAR), a practical training objective that minimizes inter-group discrepancies in feature centroids and covariances. FAR consistently improves overall AUC, ES-AUC, and subgroup performance across all datasets. Our work advances the theoretical understanding of fairness in AI systems and provides a foundation for developing more equitable algorithms. The code for analysis is publicly available at https://github.com/Harvard-AI-and-Robotics-Lab/FairnessGuarantee.