We apply a state-of-the-art membership inference attack (MIA) to systematically test the practical privacy vulnerability of fine-tuning large image classification models. We focus on understanding the properties of data sets and samples that make them vulnerable to membership inference. In terms of data set properties, we find a strong power law dependence between the number of examples per class in the data and the MIA vulnerability, as measured by true positive rate of the attack at a low false positive rate. We train a linear model to predict true positive rate based on data set properties and observe good fit for MIA vulnerability on unseen data. To analyse the phenomenon theoretically, we reproduce the result on a simplified model of membership inference that behaves similarly to our experimental data. We prove that in this model, the logarithm of the difference of true and false positive rates depends linearly on the logarithm of the number of examples per class.For an individual sample, the gradient norm is predictive of its vulnerability.
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