Effective passive membership inference attacks in federated learning against overparameterized models

This work considers the challenge of performing membership inference attacks in a federated learning setting ---for image classification--- where an adversary can only observe the communication between the central node and a single client (a passive white-box attack). Passive attacks are one of the hardest-to-detect attacks, since they can be performed without modifying how the behavior of the central server or its clients, and assumes *no access to private data instances*. The key insight of our method is empirically observing that, near parameters that generalize well in test, the gradient of large overparameterized neural network models statistically behave like high-dimensional independent isotropic random vectors. Using this insight, we devise two attacks that are often little impacted by existing and proposed defenses. Finally, we validated the hypothesis that our attack depends on the overparametrization by showing that increasing the level of overparametrization (without changing the neural network architecture) positively correlates with our attack effectiveness.