Rethinking Aggregation Error in Federated LoRA

Low-Rank Adaptation (LoRA) is the dominant approach for parameter-efficient federated fine-tuning, but independently averaging the two factor matrices across clients does not recover the average of their products. This aggregation incon-sistency has motivated a wave of mitigation methods—FFA-LoRA freezes one factor, RoLoRA alternates the frozen factor, FedEx-LoRA corrects the residual at the server—all built on the unstated assumption that the error is harmful. We revisit this assumption. We prove that the aggregation error equals the weighted cross-factor covariance, is bounded by the dispersion product, and decomposes into three geometric components dominated by subspace misalignment (>84%). To test whether the error causally harms accuracy, we introduce a controlled instrument: a per-client regularizer parameterized by strength λ, available in two equivalent forms (dispersion-product and output-space), used not as a deployable method but to vary error along a single axis. Across two model scales (RoBERTa-base 125M, DeBERTa-v3-large 435M), three seeds, and four orders of magnitude in λ, aggregation error varies by more than 30× while final accuracy varies by less than 1.5% among non-freezing methods. Factor-freezing methods that eliminate the error lose 1–3% accuracy on the smaller model; our instrument reduces error by 33–96% while matching unconstrained FedAvg with statistical equivalence (TOST, ∆=0.5%, α=0.05). The practical cost of aggregation inconsistency lies not in the error itself but in the constraints imposed to eliminate it.