# Revisiting ML Training under Fully Homomorphic Encryption: Convergence Guarantees, Differential Privacy, and Efficient Algorithms

arXiv: https://arxiv.org/abs/2605.27782 · HTML: https://mlsanity.com/paper/2605.27782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 6 of 6)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [Neural Network Training With Homomorphic Encryption](https://mlsanity.com/paper/2012.13552/) (2020)
- [Efficient Ranking, Order Statistics, and Sorting under CKKS](https://mlsanity.com/paper/2412.15126/) (2024)

## Abstract (arXiv)

We present the first theoretical convergence analysis of machine learning training under fully homomorphic encryption (FHE), combined with a differentially private (DP) training algorithm tailored to encrypted computation. Our approach improves computational efficiency over standard differentially private gradient descent (DP-GD) while achieving comparable utility. In particular, we prove convergence of approximate gradient descent using polynomial approximations of activation and loss functions, which are required for FHE compatibility. To preserve privacy in downstream tasks, we integrate differential privacy without relying on costly per-sample gradient clipping, enabling scalable encrypted learning. We also provide data-independent hyperparameter selection and theoretically grounded strategies for polynomial approximation which can be of independent interest. Together, these contributions advance the feasibility of efficient, private, and secure machine learning on sensitive data.