这篇论文提出了一个分析基于邻域的公平性审计鲁棒性的几何框架，对于理解审计的不稳定性有重要意义，值得一读。
基于邻域的公平性审计通过比较特征空间中相似个体的预测来评估个体公平性。尽管其应用广泛，但关于审计程序的鲁棒性知之甚少。本研究开发了一个几何框架，用于分析在有限扰动下基于邻域的公平性审计的鲁棒性。分析建立了邻域不变性的充分条件，量化了邻域替换如何传播到审计的不稳定性，并引入了审计波动性，这是一个在重复扰动下公平性审计预期敏感性的度量。在基准数据集上的实验支持了理论分析，并表明所提出的框架解释了基于邻域的公平性审计观察到的稳定性。
A Geometric Theory of Robust Fairness Audits
Neighborhood-based fairness audits evaluate individual fairness by comparing predictions among similar individuals in feature space. Despite their widespread use, little is known about the robustness of the auditing procedure itself. Because these audits rely on nearest neighbor relationships, small perturbations in feature space can alter local neighborhoods and produce different fairness assessments even when model predictions remain unchanged. We develop a geometric framework for analyzing the robustness of neighborhood-based fairness audits under bounded perturbations. Our analysis establishes sufficient conditions for neighborhood invariance, quantifies how neighborhood replacement propagates to audit instability, and introduces audit volatility, a measure of the expected sensitivity of fairness audits under repeated perturbations. Experiments on benchmark datasets support the theoretical analysis and show that the proposed framework explains the observed stability of neighborhood-based fairness audits.