Can LoRA Fusion Support Cross-Domain Tasks in Cloud-Edge Collaboration?

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.

Low-rank adaptation (LoRA) has emerged as a powerful tool for parameter-efficient fine-tuning of large language models (LLMs). This paper studies LoRA under a federated learning setting, enabling collaborative fine-tuning across clients while preserving parameter efficiency. We focus on a highly heterogeneous regime in which clients share only partial structure and a substantial subset may be contaminated. We propose Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR), a contamination-aware framework that relies only on preliminary local estimators. Its formulation applies broadly, from linear regression to neural network and LLM modules, whenever local adaptation can be represented by matrix-valued updates. CLAIR recovers the shared LoRA subspace and detects contaminated clients via a structured low-rank plus block-sparse decomposition. We prove exact recovery of the shared LoRA subspace in the noiseless case, stable recovery under preliminary estimation error, and consistent collaborative-set recovery under mild separation conditions. We further quantify the gain from CLAIR refinement: it reduces off-subspace estimation error through cross-client averaging while preserving client-specific variation within the shared LoRA subspace, thus improves over local fine-tuning whenever this oracle gain outweighs the costs of subspace estimation and benign-client heterogeneity. Empirically, we demonstrate the benefits of CLAIR by fine-tuning a Transformer architecture on a text-copying task. The results show accurate contamination detection and improved benign-client performance compared with local fine-tuning and non-robust federated averaging.

Amid the rapid advancement of physical-world intelligence, cloud-edge collaborative large language models (LLMs) have emerged as a promising roadmap for practical LLM deployment. However, existing cloud-edge paradigms struggle to balance global consensus with local personalization, which fails to satisfy the need for a unified knowledge foundation on the cloud and domain-specific adaptation at the edge. To address this, we introduce, for the first time, a personalized bilevel optimization framework that formalizes cloud-edge LLM collaboration as a dual structure: the upper level optimizes edge-side personalization, while the lower level governs cloud-side knowledge transfer, reaching cloud-edge evolving in coordination. We then propose CIDERS, an efficient solver that decomposes the model into a learnable backbone and a messenger. While the cloud performs knowledge transfer to the learnable backbone, the key lies in embedding global trajectories into each local personalization step via consensus-variate correction to reconcile personalization with consensus. We provide a comprehensive theoretical analysis, including a geometric characterization of the local trajectory and a full convergence guarantee, revealing an explicit trade-off structure between personalization and global convergence. Extensive experiments demonstrate that CIDERS consistently outperforms competitive baselines on the compressed edge path, with 3.1x and 1.7x gains on mathematical reasoning and code generation, respectively, and a 10% relative gain on instruction metrics. Mechanism experiments attribute these gains to early consensus-corrected coordination and task-aware distillation. Overall, CIDERS offers a viable path toward consensus-guided continuous personalization in cloud-edge LLM systems.