Curvature Clues: Decoding Deep Learning Privacy with Input Loss Curvature

In this paper, we explore the properties of loss curvature with respect to input data in deep neural networks. Curvature of loss with respect to input (termed input loss curvature) is the trace of the Hessian of the loss with respect to the input. We investigate how input loss curvature varies between train and test sets, and its implications for train-test distinguishability. We develop a theoretical framework that derives an upper bound on the train-test distinguishability based on privacy and the size of the training set. Our analysis highlights how the performance of membership inference attack (MIA) methods varies with the size of the training set, showing that curvature-based MIA outperforms other methods on sufficiently large datasets.