FedRot-LoRA: Mitigating Rotational Misalignment in Federated LoRA

Low-Rank Adaptation (LoRA) enables efficient federated fine-tuning of large language models, but its factorized parameterization creates a tension between accurate aggregation of local updates and continuity of locally optimized factors. Factor-wise aggregation incurs aggregation mismatch but better preserves factor continuity, whereas product-space reconstruction reduces this mismatch at the cost of greater factor-level initialization mismatch from newly reconstructed factors. We propose FedPA-LoRA, a product-aligned federated LoRA framework that jointly addresses these limitations and provably converges under both homogeneous and heterogeneous client ranks. Each client preserves its local factors across communication rounds and aligns its product toward a rank-specific global reference, maintaining local optimization continuity while promoting global consistency under data heterogeneity. The server aggregates heterogeneous-rank updates in the common product space and efficiently reconstructs a rank-constrained global adapter without forming the dense aggregate. This design supports client-specific computation and communication budgets. Experiments on natural language understanding and generation tasks show that FedPA-LoRA consistently outperforms representative baselines across varying levels of data heterogeneity and homogeneous- and heterogeneous-rank settings, with up to a $6.82$ percentage-point improvement in average GLUE accuracy under heterogeneous client ranks.

Federated low-rank adaptation (LoRA) enables collaborative fine-tuning of large language models without centralizing private client data. Its factorized update, however, creates a structural mismatch in federated averaging: averaging the two LoRA factors separately does not equal averaging their products. Existing exact methods resolve this issue mainly by freezing an entire factor or alternating factors across rounds, but none can update factors simultaneously without aggregation errors or expanding communication ranks. To address this fundamental problem, we present CFLoRA, a federated LoRA scheme that partitions latent LoRA channels into two complementary sets in every communication round. By ensuring that columns and rows are complementary across factors, we eliminate bilinear terms in matrix multiplications, making federated aggregation exact. Crucially, our framework also supports clients with heterogeneous rank budgets. Convergence analysis validates CFLoRA achieves $\mathcal{O}(1/\sqrt{T})$ convergence rate of the original LoRA objective in homogeneous-rank cases. Extensive experiments with RoBERTa on the GLUE benchmark and with LLaMA-3.2-3B-Instruct on commonsense reasoning tasks demonstrate that CFLoRA achieves superior performance and training efficiency compared to state-of-the-art federated LoRA baselines.

Federated LoRA enables parameter-efficient adaptation of large language models under decentralized data and limited client resources.However, directly averaging LoRA factors is representation-dependent: the same intrinsic update admits infinitely many gauge-equivalent factorizations, so factor-level aggregation can change under arbitrary coordinate choices while the underlying update remains unchanged. This reveals a semantic mismatch in existing federated LoRA aggregation rules. We propose GLoRA, a gauge-aware server representation for federated LoRA.Instead of aggregating raw factors, GLoRA estimates a consensus update subspace from client projectors and aggregates client updates in shared reference coordinates, thereby representing semantic update aggregation entirely in low-rank form. To support heterogeneous client capacities, GLoRA further provides a rank-compatible readout that instantiates adapters of different ranks from the same server state without dense update reconstruction. Experiments on GLUE and SuperNI show that GLoRA consistently outperforms federated LoRA baselines under data, resource, and task heterogeneity, including heterogeneous client ranks, sparse participation, larger backbones, and unseen-task evaluation. GLoRA also achieves a favorable efficiency--performance trade-off, suggesting that effective federated LoRA requires not merely averaging low-rank factors, but defining a semantically meaningful server-side representation for aggregation.