From Bilinear to Linear: Differentially Private Federated LoRA via Low-Dimensional Parameterization

Federated Low-Rank Adaptation (LoRA) provides an efficient solution for finetuning large language models across distributed and privacy-sensitive data. However, despite avoiding raw data sharing, federated LoRA remains vulnerable to privacy leakage through transmitted model updates. Differential privacy (DP) mitigates such leakage, but integrating DP into federated LoRA introduces two fundamental challenges: aggregation mismatch from independently averaging low-rank factors, and quadratic noise amplification when noise is injected into both factors. To address these challenges, we propose FedHSIP, a differentially private federated LoRA framework based on a unified low-dimensional parameterization. FedHSIP reformulates all LoRA parameters into a shared low-dimensional trainable vector, enabling clients to optimize and communicate only low-dimensional updates. This reformulation transforms federated LoRA from a bilinear factor aggregation problem into a unified linear parameter space, thereby eliminating aggregation mismatch and preventing the quadratic amplification of DP noise. To further handle non-IID data, we introduce a heterogeneity- and sensitivity-aware isometric projection, constructed from warm-up statistics, which groups coordinates with compatible cross-client update patterns while balancing sensitivity, update energy, and heterogeneity across the low-dimensional space. Extensive experiments on natural language understanding and generation benchmarks show that FedHSIP consistently outperforms existing federated LoRA methods under both private and non-private settings, achieving up to 3-4% improvements under differential privacy while reducing communication cost by over 80% and maintaining robustness under heterogeneous data distributions.