Deep Gradient Leakage (DGL) is a highly effective attack that recovers private training images from gradient vectors. This attack casts significant privacy challenges on distributed learning from clients with sensitive data, where clients are required to share gradients. Defending against such attacks requires but lacks an understanding of when and how privacy leakage happens, mostly because of the black-box nature of deep networks. In this paper, we propose a novel Inversion Influence Function (I$^2$F) that establishes a closed-form connection between the recovered images and the private gradients by implicitly solving the DGL problem. Compared to directly solving DGL, I$^2$F is scalable for analyzing deep networks, requiring only oracle access to gradients and Jacobian-vector products. We empirically demonstrate that I$^2$F effectively approximated the DGL generally on different model architectures, datasets, attack implementations, and noise-based defenses. With this novel tool, we provide insights into effective gradient perturbation directions, the unfairness of privacy protection, and privacy-preferred model initialization. Our codes are provided in https://github.com/illidanlab/inversion-influence-function.

翻译：深度梯度泄露（DGL）是一种高效的攻击方法，能从梯度向量中恢复私有的训练图像。该攻击对涉及客户端敏感数据（需共享梯度）的分布式学习构成了重大隐私挑战。防御此类攻击需要理解隐私泄露的时机与机理，但这一理解目前仍十分欠缺，主要源于深度网络的黑箱特性。本文提出新颖的反演影响函数（I$^2$F），通过隐式求解DGL问题，在恢复图像与私有梯度之间建立闭合形式的联系。与直接求解DGL相比，I$^2$F可扩展至深度网络分析，仅需通过预言机访问梯度与雅可比向量积。实验表明，I$^2$F能有效逼近不同模型架构、数据集、攻击实现及基于噪声的防御下的整体DGL效果。借助这一新工具，我们揭示了有效的梯度扰动方向、隐私保护不公平性及偏好隐私的模型初始化策略。代码请见 https://github.com/illidanlab/inversion-influence-function。