# A Geometric Theory of Robust Fairness Audits

arXiv: https://arxiv.org/abs/2608.24818 · HTML: https://mlsanity.com/paper/2608.24818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018)
- [Closing the AI Accountability Gap: Defining an End-to-End Framework for Internal Algorithmic Auditing](https://mlsanity.com/paper/2001.00973/) (2020)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Measurement and Fairness](https://mlsanity.com/paper/1912.05511/) (2019)
- [Training individually fair ML models with Sensitive Subspace Robustness](https://mlsanity.com/paper/1907.00020/) (2019)
- [Online Learning with an Unknown Fairness Metric](https://mlsanity.com/paper/1802.06936/) (2018)
- [Fairness Through Computationally-Bounded Awareness](https://mlsanity.com/paper/1803.03239/) (2018)
- [Sample Selection for Fair and Robust Training](https://mlsanity.com/paper/2110.14222/) (2021)
- [Probably Approximately Metric-Fair Learning](https://mlsanity.com/paper/1803.03242/) (2018)
- [Auditing ML Models for Individual Bias and Unfairness](https://mlsanity.com/paper/2003.05048/) (2020)

## Abstract (arXiv)

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.