Subspace-Constrained Federated Learning with Low-Rank Adaptation

Federated fine-tuning of foundation models with Low-Rank Adaptation (LoRA) provides an efficient solution for reducing communication and computation costs while preserving data locality. However, the direct combination of FedAvg and LoRA suffers from three key issues: limited update space, which restricts the model's effective learning capacity; inter-round state mismatch, which disrupts cross-round local optimization continuity; and a client-agnostic starting state, which slows local convergence on clients. Although recent methods mitigate the limited update space issue by merging LoRA updates into the backbone across communication rounds, inter-round state mismatch and the client-agnostic starting state remain insufficiently addressed. To address these issues, we propose FedSmoothLoRA, a federated LoRA tuning framework that preserves the enlarged update space, improves cross-round local optimization continuity, and provides a client-aware starting state for local training. At each communication round, FedSmoothLoRA constructs the local LoRA initialization using two matrices: a Round-Matching matrix that preserves cross-round local state continuity, and a Gradient-Aligned matrix that provides client-specific optimization guidance from gradient signals estimated on local data. Together, these designs enable smoother and faster convergence. Extensive experiments on image classification and natural language generation tasks demonstrate that FedSmoothLoRA consistently outperforms existing federated LoRA tuning methods. Code: https://github.com/wangzehao0704/FedSmoothLoRA

Low-rank adaptation (LoRA) represents large language model (LLM) updates with two compact matrix factors, i.e., $A$ and $B$, providing an efficient way to fine-tune large models in federated learning paradigm. Inspired by the asymmetric roles of the LoRA factors, we study whether $A$ should be shared across clients while $B$ remains client-specific (Share-A/Local-B), or whether $B$ should instead be shared while $A$ remains client-specific (Share-B/Local-A). With a least-squares surrogate, we reveal that Share-A/Local-B requires the client-specific LoRA update matrices to use a common rank-$r$ input-side space, whereas Share-B/Local-A requires a common rank-$r$ output-side space. The two strategies therefore incur different projection residuals, indicating that the preferred strategy is the one with the smaller aggregate residual across clients. With this insight, we propose Federated Adaptive Factor Sharing Low-Rank Adaptation (FedAS-LoRA), which selects the sharing side before training to enhance fine-tuning performance. To enable adaptive factor selection before training, we design a Rank-Aware Shared-Subspace Sufficiency (RSS) metric, which effectively assesses whether a shared rank-$r$ input subspace is sufficient for the local data distributions using representations extracted from a frozen LLM backbone. Experiments across different tasks, data distributions, LoRA ranks, and participation settings confirm the effectiveness of RSS and the superior performance of FedAS-LoRA.

Federated fine-tuning of large pre-trained models increasingly relies on Low-Rank Adaptation (LoRA) to reduce communication and computation, but heterogeneous clients can make adapter aggregation unstable. We identify the data-parameter interference as a geometric source of this instability. This interference is controlled by the alignment between LoRA update subspaces and client activations, suggesting that federated LoRA aggregation should be viewed not only as parameter averaging but also as subspace allocation. We propose Dynamic Subspace Boosting (Dysco), a plug-in method that allocates client-specific LoRA subspaces in a federated and dynamic manner. In each round, clients compute activation-insensitive subspaces from local representations and transmit only the resulting bases; the server then constructs client-specific merged subspaces through a closed-form solution that maximizes compatibility with other clients' insensitive directions. To handle representation drift, Dysco performs multi-round subspace boosting to preserve past update directions while adapting to future representations. We provide a convergence analysis that embeds the data-parameter interference as an aggregation-error term in a standard federated optimization bound, and prove that Dysco's server-fixed merged subspaces yield a tighter upper bound on this error. Experiments on controlled synthetic federated tasks and on MIMIC-IV clinical-note classification with Llama-3.2-1B show that Dysco substantially reduces interference, reduces the final-round synthetic training loss by up to 9 times relative to baselines under the orthogonal-subspace partition the theory identifies, improves all five tested FL algorithms by up to 4.3% on MIMIC, outperforms recent federated LoRA methods, and adds only 0.9% wall-clock overhead. Our code is available at https://github.com/illidanlab/Dysco.