# Scaling Laws for Differentially Private Language Models

arXiv: https://arxiv.org/abs/2501.18914 · HTML: https://mlsanity.com/paper/2501.18914/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2025.

## Built on by (most cited first, 22 of 22)

- [VaultGemma: A Differentially Private Gemma Model](https://mlsanity.com/paper/2510.15001/) (2025)
- [Tokens for Learning, Tokens for Unlearning: Mitigating Membership Inference Attacks in Large Language Models via Dual-Purpose Training](https://mlsanity.com/paper/2502.19726/) (2025)
- [Mitigating Unintended Memorization with LoRA in Federated Learning for LLMs](https://mlsanity.com/paper/2502.05087/) (2025)
- [ContextLeak: Auditing Leakage in Private In-Context Learning Methods](https://mlsanity.com/paper/2512.16059/) (2025)
- [Fundamental Limitations of Favorable Privacy-Utility Guarantees for DP-SGD](https://mlsanity.com/paper/2601.10237/) (2026)
- [Length Generalization Bounds for Transformers](https://mlsanity.com/paper/2603.02238/) (2026)
- [Privasis: Synthesizing the Largest "Public" Private Dataset from Scratch](https://mlsanity.com/paper/2602.03183/) (2026)
- [Efficient privacy loss accounting for subsampling and random allocation](https://mlsanity.com/paper/2602.17284/) (2026)
- [On the Price of Privacy for Language Identification and Generation](https://mlsanity.com/paper/2604.07238/) (2026)
- [Evaluating the Robustness of Chinchilla Compute-Optimal Scaling](https://mlsanity.com/paper/2509.23963/) (2025)
- [On the Gradient Complexity of Private Optimization with Private Oracles](https://mlsanity.com/paper/2511.13999/) (2025)
- [Adaptive Methods Are Preferable in High Privacy Settings: An SDE Perspective](https://mlsanity.com/paper/2603.03226/) (2026)
- [Less Random, More Private: What is the Optimal Subsampling Scheme for DP-SGD?](https://mlsanity.com/paper/2605.07072/) (2026)
- [Cocoon: A System Architecture for Differentially Private Training with Correlated Noises](https://mlsanity.com/paper/2510.07304/) (2025)
- [On Optimal Hyperparameters for Differentially Private Deep Transfer Learning](https://mlsanity.com/paper/2510.20616/) (2025)
- [Your Privacy Depends on Others: Collusion Vulnerabilities in Individual Differential Privacy](https://mlsanity.com/paper/2601.12922/) (2026)
- [Protecting Private Code in IDE Autocomplete using Differential Privacy](https://mlsanity.com/paper/2601.22935/) (2026)
- [Amplified Patch-Level Differential Privacy for Free via Random Cropping](https://mlsanity.com/paper/2603.24695/) (2026)
- [ContinuousBench: Can Differentially Private Synthetic Text Improve Capabilities?](https://mlsanity.com/paper/2606.01849/) (2026)
- [The Privacy-Hallucination Tradeoff in Differentially Private Language Models](https://mlsanity.com/paper/2609.00492/) (2026)
- [Memorisation bias in medical AI](https://mlsanity.com/paper/2609.17223/) (2026)
- [A Sharp Transition in Data Reconstruction under Differential Privacy](https://mlsanity.com/paper/2609.37344/) (2026)

## Abstract (arXiv)

Scaling laws have emerged as important components of large language model (LLM) training as they can predict performance gains through scale, and provide guidance on important hyper-parameter choices that would otherwise be expensive. LLMs also rely on large, high-quality training datasets, like those sourced from (sometimes sensitive) user data. Training models on this sensitive user data requires careful privacy protections like differential privacy (DP). However, the dynamics of DP training are significantly different, and consequently their scaling laws are not yet fully understood. In this work, we establish scaling laws that accurately model the intricacies of DP LLM training, providing a complete picture of the compute-privacy-utility tradeoffs and the optimal training configurations in many settings.