# Fair Representation Learning through Implicit Path Alignment

arXiv: https://arxiv.org/abs/2205.13316 · HTML: https://mlsanity.com/paper/2205.13316/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 51 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Learning Not to Learn: Training Deep Neural Networks with Biased Data](https://mlsanity.com/paper/1812.10352/) (2018)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [FAHT: An Adaptive Fairness-aware Decision Tree Classifier](https://mlsanity.com/paper/1907.07237/) (2019)
- [Controllable Guarantees for Fair Outcomes via Contrastive Information Estimation](https://mlsanity.com/paper/2101.04108/) (2021)
- [Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments](https://mlsanity.com/paper/2106.09913/) (2021)

## Built on by (most cited first, 22 of 22)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [When Source-Free Domain Adaptation Meets Learning with Noisy Labels](https://mlsanity.com/paper/2301.13381/) (2023)
- [On Learning Fairness and Accuracy on Multiple Subgroups](https://mlsanity.com/paper/2210.10837/) (2022)
- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothing](https://mlsanity.com/paper/2206.11423/) (2022)
- [Understanding Fairness Surrogate Functions in Algorithmic Fairness](https://mlsanity.com/paper/2310.11211/) (2023)
- [Algorithm-Dependent Bounds for Representation Learning of Multi-Source Domain Adaptation](https://mlsanity.com/paper/2304.02064/) (2023)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics](https://mlsanity.com/paper/2505.06435/) (2025)
- [Group-robust Sample Reweighting for Subpopulation Shifts via Influence Functions](https://mlsanity.com/paper/2503.07315/) (2025)
- [Intersectional Unfairness Discovery](https://mlsanity.com/paper/2405.20790/) (2024)
- [Procedural Fairness Through Decoupling Objectionable Data Generating Components](https://mlsanity.com/paper/2311.14688/) (2023)
- [Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis](https://mlsanity.com/paper/2506.00849/) (2025)
- [Pushing the Accuracy-Group Robustness Frontier with Introspective Self-play](https://mlsanity.com/paper/2302.05807/) (2023)
- [Learning Fair Representations with High-Confidence Guarantees](https://mlsanity.com/paper/2310.15358/) (2023)
- [Enhancing Fairness through Reweighting: A Path to Attain the Sufficiency Rule](https://mlsanity.com/paper/2408.14126/) (2024)
- [SoK: Data Minimization in Machine Learning](https://mlsanity.com/paper/2508.10836/) (2025)
- [From Discrete to Continuous: Deep Fair Clustering With Transferable Representations](https://mlsanity.com/paper/2403.16201/) (2024)
- [Back to the Drawing Board for Fair Representation Learning](https://mlsanity.com/paper/2405.18161/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference](https://mlsanity.com/paper/2510.21017/) (2025)

## Abstract (arXiv)

We consider a fair representation learning perspective, where optimal predictors, on top of the data representation, are ensured to be invariant with respect to different sub-groups. Specifically, we formulate this intuition as a bi-level optimization, where the representation is learned in the outer-loop, and invariant optimal group predictors are updated in the inner-loop. Moreover, the proposed bi-level objective is demonstrated to fulfill the sufficiency rule, which is desirable in various practical scenarios but was not commonly studied in the fair learning. Besides, to avoid the high computational and memory cost of differentiating in the inner-loop of bi-level objective, we propose an implicit path alignment algorithm, which only relies on the solution of inner optimization and the implicit differentiation rather than the exact optimization path. We further analyze the error gap of the implicit approach and empirically validate the proposed method in both classification and regression settings. Experimental results show the consistently better trade-off in prediction performance and fairness measurement.