Equivalent on Accuracy, Ordered in Fidelity: Aggregation under Partial Reception in Decentralized Federated Learning

In decentralized federated learning over unreliable links without retransmission, a receiver obtains only a subset of each neighbor's model coordinates with reception probability $q$, which are unobservable in advance and channel-imposed rather than designed or selected. We show that final accuracy, the standard comparison metric, fails to distinguish aggregation rules under standard annealing schedules. We propose a direct measure of aggregation fidelity, the distance between the aggregate formed under coordinate loss and its lossless counterpart, and use it to give a two-part characterization. First, fidelity separates aggregators into two families. Convex per-coordinate weights cannot amplify disagreement in any realization, whereas naive loss compensation incurs variance $\Theta ((1-q)/q)$ that is coupled to parameter magnitude rather than to the step size. This property is path-wise, so learning-rate schedules cannot change family membership, as confirmed under constant and cosine schedules. Second, within this stable family the difference between rules persists, but their visibility depends on the schedule. Final accuracy separates aggregation rules at a constant rate, but converges, or even inverts at cosine annealing. Fidelity, consensus, and convergence cost nevertheless preserve their ordering, with the fidelity gap widening monotonically from $1.56\times$ to $7.62\times$ against the strongest baseline as availability falls. Benchmarking on final accuracy under a single schedule therefore identifies a rule’s family but never the ordering within it.