# CertiFair: A Framework for Certified Global Fairness of Neural Networks

arXiv: https://arxiv.org/abs/2205.09927 · HTML: https://mlsanity.com/paper/2205.09927/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 53 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [FairGAN: Fairness-aware Generative Adversarial Networks](https://mlsanity.com/paper/1805.11202/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Training individually fair ML models with Sensitive Subspace Robustness](https://mlsanity.com/paper/1907.00020/) (2019)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [Verifying Individual Fairness in Machine Learning Models](https://mlsanity.com/paper/2006.11737/) (2020)
- [Probabilistic Verification of Fairness Properties via Concentration](https://mlsanity.com/paper/1812.02573/) (2018)
- [Perfectly Parallel Fairness Certification of Neural Networks](https://mlsanity.com/paper/1912.02499/) (2019)

## Built on by (most cited first, 17 of 17)

- [Privacy and Fairness in Federated Learning: on the Perspective of Trade-off](https://mlsanity.com/paper/2306.14123/) (2023)
- [FairProof : Confidential and Certifiable Fairness for Neural Networks](https://mlsanity.com/paper/2402.12572/) (2024)
- [The Pursuit of Fairness in Artificial Intelligence Models: A Survey](https://mlsanity.com/paper/2403.17333/) (2024)
- [Explainable Global Fairness Verification of Tree-Based Classifiers](https://mlsanity.com/paper/2209.13179/) (2022)
- [DeepBern-Nets: Taming the Complexity of Certifying Neural Networks using Bernstein Polynomial Activations and Precise Bound Propagation](https://mlsanity.com/paper/2305.13508/) (2023)
- [Relational DNN Verification With Cross Executional Bound Refinement](https://mlsanity.com/paper/2405.10143/) (2024)
- [FETA: Fairness Enforced Verifying, Training, and Predicting Algorithms for Neural Networks](https://mlsanity.com/paper/2206.00553/) (2022)
- [FairQuant: Certifying and Quantifying Fairness of Deep Neural Networks](https://mlsanity.com/paper/2409.03220/) (2024)
- [Logic Gate Neural Networks are Good for Verification](https://mlsanity.com/paper/2505.19932/) (2025)
- [Monitoring Robustness and Individual Fairness](https://mlsanity.com/paper/2506.00496/) (2025)
- [Certification of Distributional Individual Fairness](https://mlsanity.com/paper/2311.11911/) (2023)
- [gRoMA: a Tool for Measuring the Global Robustness of Deep Neural Networks](https://mlsanity.com/paper/2301.02288/) (2023)
- [Uncovering Discrimination Clusters: Quantifying and Explaining Systematic Fairness Violations](https://mlsanity.com/paper/2512.23769/) (2025)
- [TestifAI: Tomography-Based Testing for Deep Learning Systems](https://mlsanity.com/paper/2608.18900/) (2026)
- [Verifying Global Neural Network Specifications using Hyperproperties](https://mlsanity.com/paper/2306.12495/) (2023)
- [Language Models That Walk the Talk: A Framework for Formal Fairness Certificates](https://mlsanity.com/paper/2505.12767/) (2025)
- [SMiLE: Provably Enforcing Global Relational Properties in Neural Networks](https://mlsanity.com/paper/2511.07208/) (2025)

## Abstract (arXiv)

We consider the problem of whether a Neural Network (NN) model satisfies global individual fairness. Individual Fairness suggests that similar individuals with respect to a certain task are to be treated similarly by the decision model. In this work, we have two main objectives. The first is to construct a verifier which checks whether the fairness property holds for a given NN in a classification task or provide a counterexample if it is violated, i.e., the model is fair if all similar individuals are classified the same, and unfair if a pair of similar individuals are classified differently. To that end, We construct a sound and complete verifier that verifies global individual fairness properties of ReLU NN classifiers using distance-based similarity metrics. The second objective of this paper is to provide a method for training provably fair NN classifiers from unfair (biased) data. We propose a fairness loss that can be used during training to enforce fair outcomes for similar individuals. We then provide provable bounds on the fairness of the resulting NN. We run experiments on commonly used fairness datasets that are publicly available and we show that global individual fairness can be improved by 96 % without significant drop in test accuracy.