Calibration Is Not Enough: Support Restoration and Residual Correctability in Federated Long-Tailed Learning

Federated Long-Tailed learning (Fed-LT) couples global class imbalance with fragmented client label support. Exact local-prior calibration removes locally missing classes from the client's calibrated softmax competition, even when those classes are observed elsewhere in the federation. Restoring class competition, however, does not eliminate client-update heterogeneity, and the resulting residuals alone do not determine how the server should correct the aggregate update. Therefore, we propose Federated Prior Recalibration and Residual Stabilization (FedPRS). On clients, Federation-Anchored Calibration (FAC) mixes local and federation priors to restore competition over federation-supported classes while retaining local-prior information. On the server, Label-Geometric Regression (LGR) fits composition-associated update residuals and applies a bounded affine correction around FedAvg. Our analysis separates support restoration from predictive utility and shows that server correction depends jointly on affine correctability, directional alignment, and correction scale, while the proposed LGR explicitly controls deviation from the FedAvg update. FedPRS achieves the highest mean Macro-F1 among the reported baselines across the evaluated CIFAR-10/100-LT settings.