PACZero: PAC-Private Fine-Tuning of Language Models via Sign Quantization

Differentially private zeroth-order optimization (DP-ZO) enables memory-efficient private fine-tuning of large language models using only forward evaluations. Existing aggregation-based DP-ZO methods reconstruct model updates at a fixed scale, ignoring that the strength of useful signals varies throughout training. Consequently, noise-dominated updates may receive excessive weight and degrade model utility. To address this issue, we propose SAGE, a noise-aware shrinkage method that adaptively attenuates privatized estimates according to their estimated signal quality. SAGE subtracts the known Gaussian noise variance from the observed second moment to estimate the underlying signal energy, stabilizes this estimate through temporal tracking, and compares its current signal-to-noise level with a warm-up reference to derive a bounded shrinkage factor. As pure post-processing, SAGE requires neither additional privacy budget nor model queries and introduces only constant additional state. Our theoretical analysis shows that shrinkage reduces the quadratic update-risk term faster than the linear descent term, preserving useful descent while limiting the influence of noise-dominated updates. Experiments on RoBERTa-large, OPT-1.3B, and OPT-6.7B demonstrate that SAGE outperforms existing baselines in most settings under the same privacy budgets while preserving the forward-only memory efficiency of DP-ZO.

Large language models (LLMs) are commonly adapted to downstream tasks through fine-tuning, but fine-tuning data often contains sensitive information that may be leaked by the resulting model. Differential privacy (DP) offers formal protection against such leakage, yet DP fine-tuning of LLMs still suffers from substantial utility degradation due to gradient clipping and noise injection. Existing work improves this trade-off by combining DP with parameter-efficient fine-tuning methods such as LoRA, which constrain the form of updates. In this work, we study a complementary direction: selective fine-tuning, which constrains where updates are applied. We propose DP-SelFT, a framework for differentially private selective fine-tuning of LLMs. DP-SelFT addresses three DP-specific challenges in parameter selection: avoiding repeated privacy cost, improving stability under noisy estimates, and selecting parameters that remain useful under clipped and noisy updates. It first constructs a lightweight DP synthetic dataset and performs selection only on this synthetic data, so the selection stage incurs no additional privacy cost. It then conducts layer-level selection by temporarily training candidate layer subsets on a synthetic training split and evaluating them on a synthetic validation split. Crucially, this temporary training is performed under a perturbation regime matched to downstream DP fine-tuning, with worst-case perturbations of the same scale as DP noise. This favors layer subsets that are not only learnable but also robust to noisy private updates. Experiments on benchmark tasks show that DP-SelFT consistently improves the privacy--utility trade-off over existing DP fine-tuning baselines under the same privacy guarantees.

Federated learning (FL) enables the collaborative training of large-scale language models (LLMs) across edge devices while keeping user data on-device. However, FL still exposes sensitive information through client-provided gradients. Differentially private stochastic gradient descent (DP-SGD) mitigates this risk by clipping each client's contribution to a threshold $C$ and adding noise proportional to $C$. Existing adaptive clipping techniques dynamically adjust $C$ but demand tedious hyperparameter tuning, which can erode the privacy budget. In this paper, we introduce DP-LAC, a method that first estimates an initial clipping threshold within an order of magnitude of the optimum using private histogram estimation, and then adapts this threshold during training without consuming additional privacy budget or introducing new hyperparameters. Empirical results show that DP-LAC outperforms both state-of-the-art adaptive clipping methods and vanilla DP-SGD, achieving an average accuracy gain of $6.6\%$.