# Scaling Private Deep Learning with Low-Rank and Sparse Gradients

arXiv: https://arxiv.org/abs/2207.02699 · HTML: https://mlsanity.com/paper/2207.02699/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 6 Jul 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [Adversary Instantiation: Lower Bounds for Differentially Private Machine Learning](https://mlsanity.com/paper/2101.04535/) (2021)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Large Scale Private Learning via Low-rank Reparametrization](https://mlsanity.com/paper/2106.09352/) (2021)
- [Do Not Let Privacy Overbill Utility: Gradient Embedding Perturbation for Private Learning](https://mlsanity.com/paper/2102.12677/) (2021)
- [Learning the Number of Neurons in Deep Networks](https://mlsanity.com/paper/1611.06321/) (2016)
- [Bounding Training Data Reconstruction in Private (Deep) Learning](https://mlsanity.com/paper/2201.12383/) (2022)

## Built on by (most cited first, 2 of 2)

- [Equivariant Differentially Private Deep Learning: Why DP-SGD Needs Sparser Models](https://mlsanity.com/paper/2301.13104/) (2023)
- [Towards Reliable and Generalizable Differentially Private Machine Learning (Extended Version)](https://mlsanity.com/paper/2508.15141/) (2025)

## Abstract (arXiv)

Applying Differentially Private Stochastic Gradient Descent (DPSGD) to training modern, large-scale neural networks such as transformer-based models is a challenging task, as the magnitude of noise added to the gradients at each iteration scales with model dimension, hindering the learning capability significantly. We propose a unified framework, textsfLSG, that fully exploits the low-rank and sparse structure of neural networks to reduce the dimension of gradient updates, and hence alleviate the negative impacts of DPSGD. The gradient updates are first approximated with a pair of low-rank matrices. Then, a novel strategy is utilized to sparsify the gradients, resulting in low-dimensional, less noisy updates that are yet capable of retaining the performance of neural networks. Empirical evaluation on natural language processing and computer vision tasks shows that our method outperforms other state-of-the-art baselines.