# Are Two Heads the Same as One? Identifying Disparate Treatment in Fair Neural Networks

arXiv: https://arxiv.org/abs/2204.04440 · HTML: https://mlsanity.com/paper/2204.04440/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 99 references that are in the map.
- First posted on arXiv 9 Apr 2022.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Men Also Like Shopping: Reducing Gender Bias Amplification using Corpus-level Constraints](https://mlsanity.com/paper/1707.09457/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Towards Fairness in Visual Recognition: Effective Strategies for Bias Mitigation](https://mlsanity.com/paper/1911.11834/) (2019)
- [Women also Snowboard: Overcoming Bias in Captioning Models](https://mlsanity.com/paper/1803.09797/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Fair Attribute Classification through Latent Space De-biasing](https://mlsanity.com/paper/2012.01469/) (2020)
- [Fairness in Deep Learning: A Computational Perspective](https://mlsanity.com/paper/1908.08843/) (2019)
- [Assessing Gender Bias in Machine Translation -- A Case Study with Google Translate](https://mlsanity.com/paper/1809.02208/) (2018)
- [Turning a Blind Eye: Explicit Removal of Biases and Variation from Deep Neural Network Embeddings](https://mlsanity.com/paper/1809.02169/) (2018)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Why Fairness Cannot Be Automated: Bridging the Gap Between EU Non-Discrimination Law and AI](https://mlsanity.com/paper/2005.05906/) (2020)
- [Overlearning Reveals Sensitive Attributes](https://mlsanity.com/paper/1905.11742/) (2019)
- [Image Counterfactual Sensitivity Analysis for Detecting Unintended Bias](https://mlsanity.com/paper/1906.06439/) (2019)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)

## Built on by (most cited first, 10 of 10)

- [Grounding and Evaluation for Large Language Models: Practical Challenges and Lessons Learned (Survey)](https://mlsanity.com/paper/2407.12858/) (2024)
- [OxonFair: A Flexible Toolkit for Algorithmic Fairness](https://mlsanity.com/paper/2407.13710/) (2024)
- [What Constitutes a Less Discriminatory Algorithm?](https://mlsanity.com/paper/2412.18138/) (2024)
- [Are demographically invariant models and representations in medical imaging fair?](https://mlsanity.com/paper/2305.01397/) (2023)
- [Fair Text Classification via Transferable Representations](https://mlsanity.com/paper/2503.07691/) (2025)
- [I Prefer not to Say: Protecting User Consent in Models with Optional Personal Data](https://mlsanity.com/paper/2210.13954/) (2022)
- [A Note on Bias to Complete](https://mlsanity.com/paper/2402.11710/) (2024)
- [Resource-constrained Fairness](https://mlsanity.com/paper/2406.01290/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Is invariance all you need for algorithmic fairness? Removing demographic information can create new bias](https://mlsanity.com/paper/2609.32004/) (2026)

## Abstract (arXiv)

We show that deep networks trained to satisfy demographic parity often do so through a form of race or gender awareness, and that the more we force a network to be fair, the more accurately we can recover race or gender from the internal state of the network. Based on this observation, we investigate an alternative fairness approach: we add a second classification head to the network to explicitly predict the protected attribute (such as race or gender) alongside the original task. After training the two-headed network, we enforce demographic parity by merging the two heads, creating a network with the same architecture as the original network. We establish a close relationship between existing approaches and our approach by showing (1) that the decisions of a fair classifier are well-approximated by our approach, and (2) that an unfair and optimally accurate classifier can be recovered from a fair classifier and our second head predicting the protected attribute. We use our explicit formulation to argue that the existing fairness approaches, just as ours, demonstrate disparate treatment and that they are likely to be unlawful in a wide range of scenarios under US law.