CovFedAvg: Local Low-Loss Curves and Federated Model Selection

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Clients observing different parts of a prediction task may learn locally equivalent models with incompatible behavior outside their observed support. We study whether redundant models permit local low-loss paths toward a compatible shared model. CovFedAvg retains local models and curve controls on clients, fits a common endpoint through aggregated gradient contributions, and selects an actual candidate model using distributed training losses. No centralized calibration examples or client-to-client sample exchange are required. Exact selection guarantees no higher evaluated training loss than the previous model and the current-round FedAvg candidate; this is not a global-optimality, stationarity, generalization, or differential-privacy guarantee. We state conditional client-compatibility and approximate-selection bounds and retain corrected transformation identities and a separate full-gradient safeguard theorem for reference algorithms. A complementary input-support example recovers the shared absolute-value regression, while matched direct fine-tuning also solves it. Across a synthetic support task, recorded activity-recognition subjects, and participating and future gas-sensor batches, we evaluate five methods, five seeds, two network widths, and 20 rounds without calibration data. At width 16, CovFedAvg raises participating-Gas macro balanced accuracy from FedAvg's 88.88% to 89.84%; matched distributed fine-tuning reaches 91.65%. Results support feasibility and modest gains over FedAvg, but do not establish a curve-specific advantage over equally costly optimization. Exact-sum numerical experiments establish data flow; end-to-end privacy requires additional mechanisms and analysis.