Fairness Invariants: A Relational Approach to Explaining and Mitigating Fairness Bugs

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Data-driven software systems are increasingly deployed in high-stakes socio-economic domains, from criminal justice to financial lending. However, these systems often exhibit individual discrimination—unjustified disparities in which a program yields different outcomes for similar individuals who differ only in their protected attributes (e.g., race, gender, age). While existing research has focused on detecting and quantifying these bugs, there remains a critical lack of principled mechanisms to explain and localize individual fairness bugs. Current explanation techniques are largely designed for single-input decisions rather than the relational nature of discrimination, which inherently involves a comparison between an original and a counterfactual pair. We present Remi, a framework for the automated localization, explanation, and mitigation of individual discrimination. Inspired by loop-invariant synthesis in formal methods, we treat counterfactual fairness as a relational invariant discovery problem. We introduce a bidirectional relational explanation framework that learns over paired examples ( x , x ′) to identify regions of the input space where fairness is violated. Unlike traditional one-way implication pairs used in invariant inference, our approach enforces bidirectional constraints: requiring identical outcomes for both original and counterfactual samples. Remiutilizes three data-alignment techniques to infer interpretable rule-based models that act as ”fairness invariants.” These rules serve as guardrails to selectively block or relabel unfair predictions without requiring model retraining. Our evaluation on symbolic and neural network programs demonstrates that Remilocalizes ground-truth fairness bugs in over 83% of cases, significantly outperforming state-of-the-art baselines and reducing discriminatory decisions in black-box models by up to 94%.