Understanding Training-Data Leakage from Gradients in Neural Networks for ImageClassifications

Federated learning of deep learning models for supervised tasks, e.g. image classification and segmentation, has found many applications: for example in human-in-the-loop tasks such as film post-production where it enables sharing of domain expertise of human artists in an efficient and effective fashion. In many such applications, we need to protect the training data from being leaked when gradients are shared in the training process due to IP or privacy concerns. Recent works have demonstrated that it is possible to reconstruct the training data from gradients for an image-classification model when its architecture is known. However, there is still an incomplete theoretical understanding of the efficacy and failure of such attacks. In this paper, we analyse the source of training-data leakage from gradients. We formulate the problem of training data reconstruction as solving an optimisation problem iteratively for each layer. The layer-wise objective function is primarily defined by weights and gradients from the current layer as well as the output from the reconstruction of the subsequent layer, but it might also involve a ‘pull-back’ constraint from the preceding layer. Training data can be reconstructed when we solve the problem backward from the output of the network through each layer. Based on this formulation, we are able to attribute the potential leakage of the training data in a deep network to its architecture. We also propose a metric to measure the level of security of a deep learning model against gradient-based attacks on the training data.