FOCS paper: membership inference attacks can need far more reference samples than training data
roydanroy · x · 2026-11-09
A paper by Haghifam, Adam Smith and Jon Ullman (arXiv:2508.19458, presented at FOCS 2026) studies the sample complexity of membership inference (MIA) in Gaussian mean estimation.
- Setting: a learner trains on n samples from N(μ,Σ); attacks typically rely on independent reference samples from the same distribution.
- Result: matching a fully informed attacker can require Ω(n + n²ρ²) reference samples.
- Implication: first result showing attackers sometimes need many more samples than the training algorithm used — meaning practical MIAs and privacy audits may be weaker than the theoretical optimum, with direct consequences for real-world privacy auditing.
The authors present Wednesday at 4 PM at NYU Kimmel Center (FOCS 2026).
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