Tracing Bias Propagation Across Subgroups in Federated Learning

In federated learning (FL), non-adversarial systematic labeling errors at one client can propagate through the shared model and disproportionately affect subgroups at other clients. Unlike malicious attacks, these errors may be difficult to detect and require different mechanisms to mitigate. We investigate whether this bias propagation follows predictable patterns that can be accounted for when designing FL mechanisms. We show that the impact of false-negative errors on recipient client--subgroup pairs can be predicted from the global model's curvature together with source and recipient-group feature summaries, without retraining a model for each possible error. This prediction has a simple geometric interpretation: a subgroup's predicted mean logit decrease is proportional to the projection of its mean feature vector onto the target-specific propagation direction. In a 4-client IID setting, predicted and empirical subgroup rankings agree closely for two source targets (mean within-seed Spearman $0.975$ and $0.968$). Under controlled client heterogeneity, agreement remains high across 24 client--subgroup pairs ($0.974$ and $0.942$ under the strongest heterogeneity). Notably, a non-target subgroup can experience the largest degradation. These results show that in the linear setting studied here, bias propagation in FL can be structured and predictable, suggesting that FL mechanisms should account for cross-client bias propagation.