FedPA-LoRA: Product-Aligned Framework for Mitigating Aggregation and Initialization Errors in Heterogeneous Federated LoRA

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 \texttt{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 \texttt{CFLoRA} achieves $\mathcal{O}(1/\sqrt{T})$ convergence rate of the \textit{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 \texttt{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 \textbf{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.

Federated LoRA fine-tuning enables parameter-efficient adaptation of pre-trained models without sharing private data, but suffers from two fundamental mismatches under heterogeneous client data: a structural aggregation mismatch caused by independently averaging LoRA factors, and a statistical collaboration mismatch caused by enforcing a single global adapter across divergent clients. To address these issues, we propose CF-LoRA, a clustered federated LoRA fine-tuning framework that combines decoupled factor aggregation with adaptation-aware client clustering. CF-LoRA first learns a globally shared $A$ factor while retaining personalized $B_i$ factors, then identifies clients with similar adaptation patterns based on the cosine similarity of their learned $B_i$ factors, and finally performs intra-cluster $B$-factor aggregation with a frozen $A$ factor. By decoupling LoRA factor aggregation, CF-LoRA preserves the low-rank structure and mitigates the structural aggregation mismatch, while adaptation-aware clustering promotes collaboration among clients with similar adaptation patterns and reduces negative transfer caused by statistical heterogeneity. Experiments on four language tasks and four vision datasets with RoBERTa and ViT show that CF-LoRA achieves the highest average accuracy in both modalities while communicating only one LoRA factor per optimization round.