ANALYTIC FEDERATED LEARNING IS VIABLE FOR REGION-BASED OBJECT DETECTION

Federated object detection typically requires repeated exchanges of model updates, while one-shot AFL promises a single upload followed by a closed-form solve. Whether this promise extends beyond fixed-output classification is unclear because detection must handle variable proposal sets, severe class imbalance, and coupled classification and localization. We introduce an analytically solved-head framework that compiles each client's supervision into additive Gram, cross-moment, and count statistics over a shared frozen proposal representation. Aggregating these statistics exactly recovers the pooled classification and box-regression objectives for any horizontal partition, without transmitting raw images, proposal features, gradients, or locally trained detector weights. With one configuration selected on VOC2007 train/validation, the resulting detector achieves $78.48\pm 0.51$ AP50 on VOC2007 test and $75.32\pm 0.24$ on VOC2012 validation without retuning; its float32 sufficient statistics are $52.88\times$ smaller than the corresponding raw JPEGs. Additional full-split controls show stable prior calibration for $\alpha \in [4,8]$ and a 22.2-ms server solve for the selected $q=193$ system. These results show that partition-invariant, one-shot AFL can support a structured, multi-function vision task while retaining useful detection accuracy across dataset releases, establishing object detection as a viable target for AFL.