Nonparametric Variational Differential Privacy via Embedding Parameter Clipping

Large language models (LLMs) are trained on vast datasets that may contain sensitive information. Differential privacy (DP), the de facto standard for formal privacy guarantees, provides a principled framework for training LLMs with provable privacy protection. However, state-of-the-art DP training implementations rely on fast gradient clipping techniques with memory overhead $O(B \min\{T^2, d^2\})$, where $B$ is the batch size, $T$ is the sequence length, and $d$ is the model width. This becomes prohibitive as both model size and context length grow. We propose DP-SGD-RC, a novel variant of DP-SGD with randomized clipping that reduces memory and compute complexity. DP-SGD-RC leverages stochastic trace estimation methods, specifically Hutchinson's estimator[Hutchinson, 1989] and its improved variant, Hutch++[Meyer et al., 2021], to reduce the memory footprint of per-sample gradient norm estimation. We provide a tight privacy analysis showing that DP-SGD-RC achieves noise multipliers competitive with deterministic clipping. Experiments fine-tuning Llama~3.2-1B on long-context benchmarks spanning classification, question answering, and summarization tasks demonstrate that DP-SGD-RC matches baseline utility while significantly reducing memory and compute requirements.

Differential privacy provides formal privacy guarantees for training neural networks on sensitive data, while Bayesian deep learning offers a principled framework for uncertainty-aware prediction. Combining these two objectives remains challenging, as privacy noise can interact with the stochasticity introduced by Bayesian posterior sampling. In this work, we investigate differentially private variational Bayesian learning through the Improved Variational Online Newton (IVON) optimizer. We introduce DP-IVON-Gradsq, a private variant of IVON. The proposed method constructs its curvature estimate from the privatized gradient using a noise-corrected squared-gradient estimator, reducing the direct interaction between posterior-sampling noise and privacy noise while preserving the Adam-like computational efficiency of IVON. We evaluate DP-IVON-Gradsq on CIFAR-10 against the standard private optimizers DP-SGD and DP-Adam over a range of privacy budgets. The results show that DP-IVON-Gradsq is competitive under weak-to-moderate privacy constraints, i.e., large-to-moderate values of $\varepsilon$, while degrading under strong privacy. Code is available at https://github.com/NourJamoussi/DP-IVON-Gradsq.git.

Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate DP perturbation into the inference, they are limited to specific types of simple probabilistic models. In this work, we propose a novel method for noise-aware approximate Bayesian inference based on stochastic gradient variational inference which can also be applied to high-dimensional and non-conjugate models. We also propose a more accurate evaluation method for noise-aware posteriors. Empirically, our inference method has similar performance to existing methods in the domain where they are applicable. Outside this domain, we obtain accurate coverages on high-dimensional Bayesian linear regression and well-calibrated predictive probabilities on Bayesian logistic regression with the UCI Adult dataset.