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

Understanding Deep Gradient Leakage via Inversion Influence Functions