Wireless Federated Multi-Task LLM Fine-Tuning via Sparse-and-Orthogonal LoRA

Decentralized federated learning (DFL) based on low-rank adaptation (LoRA) enables mobile devices with multi-task datasets to collaboratively fine-tune a large language model (LLM) by exchanging locally updated parameters with a subset of neighboring devices via wireless connections for knowledge integration.However, directly aggregating parameters fine-tuned on heterogeneous datasets induces three primary issues across the DFL life-cycle: (i) \textit{catastrophic knowledge forgetting during fine-tuning process}, arising from conflicting update directions caused by data heterogeneity; (ii) \textit{inefficient communication and convergence during model aggregation process}, due to bandwidth-intensive redundant model transmissions; and (iii) \textit{multi-task knowledge interference during inference process}, resulting from incompatible knowledge representations coexistence during inference. To address these issues in a fully decentralized scenario, we first propose a sparse-and-orthogonal LoRA that ensures orthogonality between model updates to eliminate direction conflicts during fine-tuning.Then, we analyze how device connection topology affects multi-task performance, prompting a cluster-based topology design during aggregation.Finally, we propose an implicit mixture of experts (MoE) mechanism to avoid the coexistence of incompatible knowledge during inference. Simulation results demonstrate that the proposed approach effectively reduces communication resource consumption by up to $73\%$ and enhances average performance by $5\%$ compared with the traditional LoRA method.