Robust Privacy: Inference-Stage Privacy through Certified Robustness

Abstract

An adversary observing a model's released prediction can infer sensitive attributes of the queried input, or even reconstruct representatives of the model's training data. The inference interface thus acts as a side channel for privacy leakage. We introduce Robust Privacy (RP), an inference-stage privacy notion inspired by certified robustness: if a model's prediction is provably invariant within a radius-$R$ neighborhood around an input $x$ with confidence at least $1-\alpha$, then $x$ enjoys $(R,\alpha)$-Robust Privacy, under which we prove that any adversary observing the released prediction has at most $\alpha/2$ advantage in distinguishing $x$ from any input within distance $R$ of $x$. Building on RP, we formalize Robust Attribute Privacy (RAP), an attribute-level privacy notion that characterizes the set of sensitive-attribute values that remain compatible with a released prediction. On a classification task, RP increases the median length of the RAP-compatible inference interval from $23.50$ to $29.96$, reducing attribute-inference precision. Model inversion attacks, often treated as a training-stage threat, in fact rely on fine-grained input-output dependence signals leaked through the inference interface; RP masks these signals at the inference stage, reducing attack success rate (ASR) from $73\%$ to $4\%$ on a black-box inversion attack. This direct targeting of the leakage channel enables RP to dominate DP-SGD and randomized response in the privacy-utility tradeoff space: RP retains $98.4\%$ accuracy at $21\%$ ASR, whereas DP-SGD must drop accuracy to $61.7\%$ to reach a comparable ASR. Across both experiments, increasing the smoothing sample size $N$ at fixed noise scale strengthens privacy and improves utility together. Finally, we examine model distillation as a scope boundary and show that RP mitigates attribute-level and instance-level inference-stage privacy leakage.