MPT: Missing Prototype Tracking via Barycentric Reconstruction in Vehicular Federated Learning

Cross-vehicle federated learning enables vehicles to collaboratively improve perception models while keeping locally collected driving data private. However, vehicle participation is transient, and a vehicle may depart before training converges while permanently taking its local data. When this departing vehicle holds most samples of a target class, the class becomes rare in the remaining FL network, and its recognition can silently degrade as the shared backbone continues to evolve. Recovering the class is difficult since the few remaining samples provide a noisy prototype estimate, while FL privacy constraints prevent centralized access to raw data or per-sample features. This paper presents MPT, a cross-vehicle FL framework that maintains rare-class recognition by reconstructing its prototype at every round from privacy-preserving class-level statistics. MPT combines a barycentric decomposition that tracks drift shared with remaining-class prototypes, a covariance-based residual prediction that estimates out-of-span drift, and an adaptive calibration that weighs the remaining rare-class samples according to their reliability. We evaluate MPT on three vehicle classification tasks and four backbones against representative calibration and drift-compensation baselines. MPT outperforms all baselines in rare class F1, reaching 0.516 on the nuImages dataset with only 1\% of rare-class samples remaining, without raw data, per-sample features, or retraining.