Membership inference attacks (MIAs) are used to test practical privacy of machine learning models. MIAs complement formal guarantees from differential privacy (DP) under a more realistic adversary model. We analyse MIA vulnerability of fine-tuned neural networks both empirically and theoretically, the latter using a simplified model of fine-tuning. We show that the vulnerability of non-DP models when measured as the attacker advantage at fixed false positive rate reduces according to a simple power law as the number of examples per class increases, even for the most vulnerable points, but the dataset size needed for adequate protection of the most vulnerable points is very large.
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