Differentially Private Stochastic Gradient Descent (DP-SGD) is a key method for applying privacy in the training of deep learning models. This 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; we observe that the $\epsilon d$-privacy guarantee does not require a $\delta>0$ term but degrades smoothly according to the dissimilarity of the input gradients. As $\epsilon$s between these different frameworks cannot be directly compared, we examine empirical privacy calibration mechanisms that go beyond previous work on empirically calibrating privacy within standard DP frameworks using membership inference attacks (MIA); we show that a combination of enhanced MIA and reconstruction attacks provides a suitable method for privacy calibration. 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 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向梯度添加各向同性高斯噪声，这可能导致梯度在各个方向上受到扰动，从而损害效用。然而，度量差分隐私（Metric DP）能够基于任意度量提供替代机制，这些机制可能更适合保留效用。本文通过基于冯·米塞斯-费舍尔（VMF）分布的机制应用方向性隐私，以角距离扰动梯度，从而大致保留梯度方向。我们证明，这为深度学习训练提供了ε-DP和εd-隐私，而非高斯机制的(ε, δ)-隐私；我们观察到，εd-隐私保证不需要δ>0项，而是根据输入梯度的相异性平滑退化。由于不同框架下的ε值无法直接比较，我们研究了超越先前工作中使用成员推断攻击（MIA）在标准DP框架内经验校准隐私的经验隐私校准机制；我们证明，增强型MIA与重构攻击的组合为隐私校准提供了合适的方法。在关键数据集上的实验表明，VMF机制在效用-隐私权衡方面可比高斯机制表现更优。特别地，我们的实验通过两种方法抵御重构和成员推断的能力，直接比较了它们之间的隐私保护水平。