Data Reconstruction Attacks and Defenses: A Systematic Evaluation

Reconstruction attacks and defenses are essential in understanding the data leakage problem in machine learning. However, prior work has centered around empirical observations of gradient inversion attacks, lacks theoretical justifications, and cannot disentangle the usefulness of defending methods from the computational limitation of attacking methods. In this work, we propose to view the problem as an inverse problem, enabling us to theoretically, quantitatively, and systematically evaluate the data reconstruction problem. On various defense methods, we derived the algorithmic upper bound and the matching (in feature dimension and model width) information-theoretical lower bound on the reconstruction error for two-layer neural networks. To complement the theoretical results and investigate the utility-privacy trade-off, we defined a natural evaluation metric of the defense methods with similar utility loss among the strongest attacks. We further propose a strong reconstruction attack that helps update some previous understanding of the strength of defense methods under our proposed evaluation metric.