FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911230568955904 |
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| author | Lee, Seanie Park, Sangwoo Lee, Dong Bok Wagner, Dominik Seong, Haebin Bocklet, Tobias Lee, Juho Hwang, Sung Ju |
| author_facet | Lee, Seanie Park, Sangwoo Lee, Dong Bok Wagner, Dominik Seong, Haebin Bocklet, Tobias Lee, Juho Hwang, Sung Ju |
| contents | Low-Rank Adaptation (LoRA), which introduces a product of two trainable low-rank matrices into frozen pre-trained weights, is widely used for efficient fine-tuning of language models in federated learning (FL). However, when combined with differentially private stochastic gradient descent (DP-SGD), LoRA faces substantial noise amplification: DP-SGD perturbs per-sample gradients, and the matrix multiplication of the LoRA update ($BA$) intensifies this effect. Freezing one matrix (e.g., $A$) reduces the noise but restricts model expressiveness, often resulting in suboptimal adaptation. To address this, we propose $\texttt{FedSVD}$, a simple yet effective method that introduces a global reparameterization based on singular value decomposition (SVD). In our approach, each client optimizes only the $B$ matrix and transmits it to the server. The server aggregates the $B$ matrices, computes the product $BA$ using the previous $A$, and refactorizes the result via SVD. This yields a new adaptive $A$ composed of the orthonormal right singular vectors of $BA$, and an updated $B$ containing the remaining SVD components. This reparameterization avoids quadratic noise amplification, while allowing $A$ to better capture the principal directions of the aggregate updates. Moreover, the orthonormal structure of $A$ bounds the gradient norms of $B$ and preserves more signal under DP-SGD, as confirmed by our theoretical analysis. As a result, $\texttt{FedSVD}$ consistently improves stability and performance across a variety of privacy settings and benchmarks, outperforming relevant baselines under both private and non-private regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA Lee, Seanie Park, Sangwoo Lee, Dong Bok Wagner, Dominik Seong, Haebin Bocklet, Tobias Lee, Juho Hwang, Sung Ju Machine Learning Artificial Intelligence Low-Rank Adaptation (LoRA), which introduces a product of two trainable low-rank matrices into frozen pre-trained weights, is widely used for efficient fine-tuning of language models in federated learning (FL). However, when combined with differentially private stochastic gradient descent (DP-SGD), LoRA faces substantial noise amplification: DP-SGD perturbs per-sample gradients, and the matrix multiplication of the LoRA update ($BA$) intensifies this effect. Freezing one matrix (e.g., $A$) reduces the noise but restricts model expressiveness, often resulting in suboptimal adaptation. To address this, we propose $\texttt{FedSVD}$, a simple yet effective method that introduces a global reparameterization based on singular value decomposition (SVD). In our approach, each client optimizes only the $B$ matrix and transmits it to the server. The server aggregates the $B$ matrices, computes the product $BA$ using the previous $A$, and refactorizes the result via SVD. This yields a new adaptive $A$ composed of the orthonormal right singular vectors of $BA$, and an updated $B$ containing the remaining SVD components. This reparameterization avoids quadratic noise amplification, while allowing $A$ to better capture the principal directions of the aggregate updates. Moreover, the orthonormal structure of $A$ bounds the gradient norms of $B$ and preserves more signal under DP-SGD, as confirmed by our theoretical analysis. As a result, $\texttt{FedSVD}$ consistently improves stability and performance across a variety of privacy settings and benchmarks, outperforming relevant baselines under both private and non-private regimes. |
| title | FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2505.12805 |