Instance-wise Batch Label Restoration via Gradients in Federated Learning

Gradient inversion attacks have posed a serious threat to the privacy of federated learning. The attacks search for the optimal pair of input and label best matching the shared gradients and the search space of the attacks can be reduced by pre-restoring labels. Recently, label restoration technique allows for the extraction of labels from gradients analytically, but even the state-of-the-art remains limited to identify the presence of categories (i.e., the class-wise label restoration). This work considers the more real-world settings, where there are multiple instances of each class in a training batch. An analytic method is proposed to perform instance-wise batch label restoration from only the gradient of the final layer. On the basis of the approximate recovered class-wise embeddings and post-softmax probabilities, we establish linear equations of the gradients, probabilities and labels to derive the Number of Instances (NoI) per class by the Moore-Penrose pseudoinverse algorithm. Our experimental evaluations reach over 99% Label existence Accuracy (LeAcc) and exceed 96% Label number Accuracy (LnAcc) in most cases on three image datasets and four classification models. The two metrics are used to evaluate class-wise and instance-wise label restoration accuracy, respectively. And the recovery is made feasible even with a batch size of 4096 and partially negative activations (e.g., Leaky ReLU and Swish). Furthermore, we demonstrate that our method facilitates the existing gradient inversion attacks by exploiting the recovered labels, with an increase of 6-7 in PSNR on both MNIST and CIFAR100. Our code is available at https://github.com/BUAA-CST/iLRG.