# Directional Privacy for Deep Learning

arXiv: https://arxiv.org/abs/2211.04686 · HTML: https://mlsanity.com/paper/2211.04686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 85 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 30 of 43)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [ML-Leaks: Model and Data Independent Membership Inference Attacks and Defenses on Machine Learning Models](https://mlsanity.com/paper/1806.01246/) (2018)
- [Large Language Models Can Be Strong Differentially Private Learners](https://mlsanity.com/paper/2110.05679/) (2021)
- [Label-Only Membership Inference Attacks](https://mlsanity.com/paper/2007.14321/) (2020)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [Membership Inference Attacks on Machine Learning: A Survey](https://mlsanity.com/paper/2103.07853/) (2021)
- [Enhanced Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/2111.09679/) (2021)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Auditing Differentially Private Machine Learning: How Private is Private SGD?](https://mlsanity.com/paper/2006.07709/) (2020)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [PIPAL: a Large-Scale Image Quality Assessment Dataset for Perceptual Image Restoration](https://mlsanity.com/paper/2007.12142/) (2020)
- [On the Importance of Difficulty Calibration in Membership Inference Attacks](https://mlsanity.com/paper/2111.08440/) (2021)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [Tempered Sigmoid Activations for Deep Learning with Differential Privacy](https://mlsanity.com/paper/2007.14191/) (2020)
- [Privacy- and Utility-Preserving Textual Analysis via Calibrated Multivariate Perturbations](https://mlsanity.com/paper/1910.08902/) (2019)
- [DP-CGAN: Differentially Private Synthetic Data and Label Generation](https://mlsanity.com/paper/2001.09700/) (2020)
- [Large-Scale Differentially Private BERT](https://mlsanity.com/paper/2108.01624/) (2021)
- [Comprehensive Privacy Analysis of Deep Learning: Passive and Active White-box Inference Attacks against Centralized and Federated Learning](https://mlsanity.com/paper/1812.00910/) (2018)

## Built on by (most cited first, 1 of 1)

- [What is the Cost of Differential Privacy for Deep Learning-Based Trajectory Generation?](https://mlsanity.com/paper/2506.09312/) (2025)

## Abstract (arXiv)

Differentially Private Stochastic Gradient Descent (DP-SGD) is a key method for applying privacy in the training of deep learning models. It applies isotropic Gaussian noise to gradients during training, which can perturb these gradients in any direction, damaging utility. Metric DP, however, can provide alternative mechanisms based on arbitrary metrics that might be more suitable for preserving utility. In this paper, we apply textitdirectional privacy, via a mechanism based on the von Mises-Fisher (VMF) distribution, to perturb gradients in terms of textitangular distance so that gradient direction is broadly preserved. We show that this provides both ε-DP and ε d-privacy for deep learning training, rather than the (ε, δ)-privacy of the Gaussian mechanism. Experiments on key datasets then indicate that the VMF mechanism can outperform the Gaussian in the utility-privacy trade-off. In particular, our experiments provide a direct empirical comparison of privacy between the two approaches in terms of their ability to defend against reconstruction and membership inference.