# Uncovering Discrimination Clusters: Quantifying and Explaining Systematic Fairness Violations

arXiv: https://arxiv.org/abs/2512.23769 · HTML: https://mlsanity.com/paper/2512.23769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 59 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 28 of 28)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Bias in Machine Learning Software: Why? How? What to do?](https://mlsanity.com/paper/2105.12195/) (2021)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [Automated Directed Fairness Testing](https://mlsanity.com/paper/1807.00468/) (2018)
- [Do the Machine Learning Models on a Crowd Sourced Platform Exhibit Bias? An Empirical Study on Model Fairness](https://mlsanity.com/paper/2005.12379/) (2020)
- [Verifying Individual Fairness in Machine Learning Models](https://mlsanity.com/paper/2006.11737/) (2020)
- [Perfectly Parallel Fairness Certification of Neural Networks](https://mlsanity.com/paper/1912.02499/) (2019)
- [Characterizing Intersectional Group Fairness with Worst-Case Comparisons](https://mlsanity.com/paper/2101.01673/) (2021)
- [NeuronFair: Interpretable White-Box Fairness Testing through Biased Neuron Identification](https://mlsanity.com/paper/2112.13214/) (2021)
- [Fairness-aware Configuration of Machine Learning Libraries](https://mlsanity.com/paper/2202.06196/) (2022)
- [Towards Proving the Adversarial Robustness of Deep Neural Networks](https://mlsanity.com/paper/1709.02802/) (2017)
- [Latent Imitator: Generating Natural Individual Discriminatory Instances for Black-Box Fairness Testing](https://mlsanity.com/paper/2305.11602/) (2023)
- [Fairify: Fairness Verification of Neural Networks](https://mlsanity.com/paper/2212.06140/) (2022)
- [Automated Test Generation to Detect Individual Discrimination in AI Models](https://mlsanity.com/paper/1809.03260/) (2018)
- [FairMask: Better Fairness via Model-based Rebalancing of Protected Attributes](https://mlsanity.com/paper/2110.01109/) (2021)
- [CertiFair: A Framework for Certified Global Fairness of Neural Networks](https://mlsanity.com/paper/2205.09927/) (2022)
- [Adaptive Fairness Improvement Based on Causality Analysis](https://mlsanity.com/paper/2209.07190/) (2022)
- [NeuFair: Neural Network Fairness Repair with Dropout](https://mlsanity.com/paper/2407.04268/) (2024)
- [Information-Theoretic Testing and Debugging of Fairness Defects in Deep Neural Networks](https://mlsanity.com/paper/2304.04199/) (2023)
- [Certifying the Fairness of KNN in the Presence of Dataset Bias](https://mlsanity.com/paper/2307.08722/) (2023)
- [FairLay-ML: Intuitive Debugging of Fairness in Data-Driven Social-Critical Software](https://mlsanity.com/paper/2407.01423/) (2024)
- [FairQuant: Certifying and Quantifying Fairness of Deep Neural Networks](https://mlsanity.com/paper/2409.03220/) (2024)
- [Fairness Testing through Extreme Value Theory](https://mlsanity.com/paper/2501.11597/) (2025)

## Built on by (most cited first, 1 of 1)

- [Fairness Invariants: A Relational Approach to Explaining and Mitigating Fairness Bugs](https://mlsanity.com/paper/2608.26209/) (2026)

## Abstract (arXiv)

Fairness in algorithmic decision-making is often framed in terms of individual fairness, which requires that similar individuals receive similar outcomes. A system violates individual fairness if there exists a pair of inputs differing only in protected attributes (such as race or gender) that lead to significantly different outcomes-for example, one favorable and the other unfavorable. While this notion highlights isolated instances of unfairness, it fails to capture broader patterns of systematic or clustered discrimination that may affect entire subgroups. We introduce and motivate the concept of discrimination clustering, a generalization of individual fairness violations. Rather than detecting single counterfactual disparities, we seek to uncover regions of the input space where small perturbations in protected features lead to k-significantly distinct clusters of outcomes. That is, for a given input, we identify a local neighborhood-differing only in protected attributes-whose members' outputs separate into many distinct clusters. These clusters reveal significant arbitrariness in treatment solely based on protected attributes that help expose patterns of algorithmic bias that elude pairwise fairness checks. We present HyFair, a hybrid technique that combines formal symbolic analysis (via SMT and MILP solvers) to certify individual fairness with randomized search to discover discriminatory clusters. This combination enables both formal guarantees-when no counterexamples exist-and the detection of severe violations that are computationally challenging for symbolic methods alone. Given a set of inputs exhibiting high k-unfairness, we introduce a novel explanation method to generate interpretable, decision-tree-style artifacts. Our experiments demonstrate that HyFair outperforms state-of-the-art fairness verification and local explanation methods.