PRISM: Gauge-Invariant Tangent-Space Differentially Private LoRA
Applying differential privacy (DP) via DP-SGD to Low-Rank Adaptation (LoRA) is a natural approach for privacy-preserving fine-tuning. However, LoRA's low-rank parameterization poses a fundamental challenge. In LoRA, each trainable update is represented as a low-rank matrix $Z = AB^\top$, but this factorization is inherently non-identifiable: many factor pairs $(A,B)$ represent the same update $Z$. As a result, applying DP-SGD directly to the factors induces gauge-dependent perturbations on $Z$, and we show that this naive DP-LoRA can lead to unbounded noise amplification. We propose PRISM, an intrinsic DP mechanism for LoRA that is gauge invariant by construction, avoids bilinear noise am...
| Authors | Shihao Wang, Xueru Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 31 May 2026 |
| Last updated at source | 31 May 2026 |
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