# Fair Dataset Distillation via Cross-Group Barycenter Alignment

arXiv: https://arxiv.org/abs/2605.00185 · HTML: https://mlsanity.com/paper/2605.00185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Towards Fairness in Visual Recognition: Effective Strategies for Bias Mitigation](https://mlsanity.com/paper/1911.11834/) (2019)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Dataset Condensation via Efficient Synthetic-Data Parameterization](https://mlsanity.com/paper/2205.14959/) (2022)
- [FairGAN: Fairness-aware Generative Adversarial Networks](https://mlsanity.com/paper/1805.11202/) (2018)
- [Improved Distribution Matching for Dataset Condensation](https://mlsanity.com/paper/2307.09742/) (2023)
- [Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent](https://mlsanity.com/paper/1802.01737/) (2018)
- [Fair Feature Distillation for Visual Recognition](https://mlsanity.com/paper/2106.04411/) (2021)
- [Coresets for Clustering with Fairness Constraints](https://mlsanity.com/paper/1906.08484/) (2019)
- [Learning Fair Classifiers with Partially Annotated Group Labels](https://mlsanity.com/paper/2111.14581/) (2021)
- [Training Gaussian Mixture Models at Scale via Coresets](https://mlsanity.com/paper/1703.08110/) (2017)
- [On Learning Fairness and Accuracy on Multiple Subgroups](https://mlsanity.com/paper/2210.10837/) (2022)
- [Dataset Distillation by Automatic Training Trajectories](https://mlsanity.com/paper/2407.14245/) (2024)
- [Towards Optimal Lower Bounds for k-median and k-means Coresets](https://mlsanity.com/paper/2202.12793/) (2022)
- [Sets Clustering](https://mlsanity.com/paper/2003.04135/) (2020)
- [On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications](https://mlsanity.com/paper/2007.10137/) (2020)
- [Provable Data Subset Selection For Efficient Neural Network Training](https://mlsanity.com/paper/2303.05151/) (2023)
- [Neural Spectral Decomposition for Dataset Distillation](https://mlsanity.com/paper/2408.16236/) (2024)
- [Fast Regression for Structured Inputs](https://mlsanity.com/paper/2203.07557/) (2022)
- [Group Distributionally Robust Dataset Distillation with Risk Minimization](https://mlsanity.com/paper/2402.04676/) (2024)
- [Distilling Long-tailed Datasets](https://mlsanity.com/paper/2408.14506/) (2024)

## Abstract (arXiv)

Dataset Distillation aims to compress a large dataset into a small synthetic one while maintaining predictive performance. We show that as different demographic groups exhibit distinct predictive patterns, the distillation process struggles to simultaneously preserve informative signals for all subgroups, regardless of whether group sizes are mildly or severely imbalanced. Consequently, models trained on distilled data can experience substantial performance drops for certain subgroups, leading to fairness gaps. Crucially, these gaps do not disappear by merely correcting group imbalance, since they stem from fundamental mismatches in subgroup predictive patterns rather than from sample-size disparities alone. We therefore formally analyze the interaction between these two sources of bias and cast the solution as identifying a group-imbalance-agnostic barycenter of the predictive information that induces similar representations across all subgroups. By distilling toward this shared aggregate representation, we show that group fairness concerns can be reduced. Our approach is compatible with existing distillation methods, and empirical results show that it substantially reduces bias introduced by dataset distillation. Code is available at https://github.com/mhmoslemi/COBRA.