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 \textit{directional privacy}, via a mechanism based on the von Mises-Fisher (VMF) distribution, to perturb gradients in terms of \textit{angular distance} so that gradient direction is broadly preserved. We show that this provides both $\epsilon$-DP and $\epsilon d$-privacy for deep learning training, rather than the $(\epsilon, \delta)$-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.

翻译：差分隐私随机梯度下降（DP-SGD）是在深度学习模型训练中应用隐私保护的关键方法。该方法在训练过程中对梯度施加各向同性的高斯噪声，这种噪声可能从任意方向扰动梯度，从而损害模型的效用。然而，度量差分隐私（Metric DP）能够基于任意度量提供替代机制，这些机制可能更有利于维护效用。本文通过基于冯·米塞斯-费舍尔（VMF）分布的机制应用\textit{定向隐私}，以\textit{角度距离}扰动梯度，从而大致保持梯度方向。研究表明，该机制为深度学习训练提供了$\epsilon$-DP和$\epsilon d$-隐私保护，而非高斯机制的$(\epsilon, \delta)$-隐私保护。关键数据集上的实验表明，VMF机制在效用与隐私的权衡中优于高斯机制。具体而言，我们的实验通过防御重建攻击和成员推断攻击的能力，对两种方法的隐私保护效果进行了直接实证比较。