Efficient DP-SGD for LLMs with Randomized 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 layer width. This becomes prohibitive as both model width and context length grow. We propose DP-SGD-RC, a novel variant of DP-SGD with *randomized clipping* that reduces memory and compute overhead. DP-SGD-RC leverages *stochastic trace estimation* methods, specifically *Hutchinson's estimator* and its improved variant, Hutch$^{++}$, 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.