# Individual Fairness Guarantees for Neural Networks

arXiv: https://arxiv.org/abs/2205.05763 · HTML: https://mlsanity.com/paper/2205.05763/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 21 of 21)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Bias Out-of-the-Box: An Empirical Analysis of Intersectional Occupational Biases in Popular Generative Language Models](https://mlsanity.com/paper/2102.04130/) (2021)
- [Globally-Robust Neural Networks](https://mlsanity.com/paper/2102.08452/) (2021)
- [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)
- [Two Simple Ways to Learn Individual Fairness Metrics from Data](https://mlsanity.com/paper/2006.11439/) (2020)
- [Metric Learning for Individual Fairness](https://mlsanity.com/paper/1906.00250/) (2019)
- [CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks](https://mlsanity.com/paper/1811.12395/) (2018)
- [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)
- [Probabilistic Safety for Bayesian Neural Networks](https://mlsanity.com/paper/2004.10281/) (2020)
- [Bayesian Inference with Certifiable Adversarial Robustness](https://mlsanity.com/paper/2102.05289/) (2021)
- [Provably Fair Representations](https://mlsanity.com/paper/1710.04394/) (2017)
- [Individual Fairness Revisited: Transferring Techniques from Adversarial Robustness](https://mlsanity.com/paper/2002.07738/) (2020)

## Built on by (most cited first, 23 of 23)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [Robust Explanation Constraints for Neural Networks](https://mlsanity.com/paper/2212.08507/) (2022)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [CertiFair: A Framework for Certified Global Fairness of Neural Networks](https://mlsanity.com/paper/2205.09927/) (2022)
- [FairProof : Confidential and Certifiable Fairness for Neural Networks](https://mlsanity.com/paper/2402.12572/) (2024)
- [BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programming](https://mlsanity.com/paper/2306.10742/) (2023)
- [Adversarial Robustness Certification for Bayesian Neural Networks](https://mlsanity.com/paper/2306.13614/) (2023)
- [When to Trust AI: Advances and Challenges for Certification of Neural Networks](https://mlsanity.com/paper/2309.11196/) (2023)
- [FETA: Fairness Enforced Verifying, Training, and Predicting Algorithms for Neural Networks](https://mlsanity.com/paper/2206.00553/) (2022)
- [Causal Adversarial Perturbations for Individual Fairness and Robustness in Heterogeneous Data Spaces](https://mlsanity.com/paper/2308.08938/) (2023)
- [Procedural Fairness in Machine Learning](https://mlsanity.com/paper/2404.01877/) (2024)
- [FairQuant: Certifying and Quantifying Fairness of Deep Neural Networks](https://mlsanity.com/paper/2409.03220/) (2024)
- [Individual Fairness in Bayesian Neural Networks](https://mlsanity.com/paper/2304.10828/) (2023)
- [Monitoring Robustness and Individual Fairness](https://mlsanity.com/paper/2506.00496/) (2025)
- [Use Perturbations when Learning from Explanations](https://mlsanity.com/paper/2303.06419/) (2023)
- [Certification of Distributional Individual Fairness](https://mlsanity.com/paper/2311.11911/) (2023)
- [Verifying the Generalization of Deep Learning to Out-of-Distribution Domains](https://mlsanity.com/paper/2406.02024/) (2024)
- [Emulating Full Participation: An Effective and Fair Client Selection Strategy for Federated Learning](https://mlsanity.com/paper/2405.13584/) (2024)
- [Correct-By-Construction: Certified Individual Fairness through Neural Network Training](https://mlsanity.com/paper/2508.15642/) (2025)
- [Analyzing Fairness of Neural Network Prediction via Counterfactual Dataset Generation](https://mlsanity.com/paper/2602.10457/) (2026)
- [Certification-Based Differentially Private Learning](https://mlsanity.com/paper/2609.39629/) (2026)
- [Tightening convex relaxations of trained neural networks: a unified approach for convex and S-shaped activations](https://mlsanity.com/paper/2410.23362/) (2024)
- [SMiLE: Provably Enforcing Global Relational Properties in Neural Networks](https://mlsanity.com/paper/2511.07208/) (2025)

## Abstract (arXiv)

We consider the problem of certifying the individual fairness (IF) of feed-forward neural networks (NNs). In particular, we work with the ε-δ-IF formulation, which, given a NN and a similarity metric learnt from data, requires that the output difference between any pair of ε-similar individuals is bounded by a maximum decision tolerance δ ≥ 0. Working with a range of metrics, including the Mahalanobis distance, we propose a method to overapproximate the resulting optimisation problem using piecewise-linear functions to lower and upper bound the NN's non-linearities globally over the input space. We encode this computation as the solution of a Mixed-Integer Linear Programming problem and demonstrate that it can be used to compute IF guarantees on four datasets widely used for fairness benchmarking. We show how this formulation can be used to encourage models' fairness at training time by modifying the NN loss, and empirically confirm our approach yields NNs that are orders of magnitude fairer than state-of-the-art methods.