# How does promoting the minority fraction affect generalization? A theoretical study of the one-hidden-layer neural network on group imbalance

arXiv: https://arxiv.org/abs/2403.07310 · HTML: https://mlsanity.com/paper/2403.07310/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 96 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 30 of 59)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Counterfactual Fairness in Text Classification through Robustness](https://mlsanity.com/paper/1809.10610/) (2018)
- [When Do Neural Networks Outperform Kernel Methods?](https://mlsanity.com/paper/2006.13409/) (2020)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [M2m: Imbalanced Classification via Major-to-minor Translation](https://mlsanity.com/paper/2004.00431/) (2020)
- [Feature Purification: How Adversarial Training Performs Robust Deep Learning](https://mlsanity.com/paper/2005.10190/) (2020)
- [Spurious Local Minima are Common in Two-Layer ReLU Neural Networks](https://mlsanity.com/paper/1712.08968/) (2017)
- [The Majority Can Help The Minority: Context-rich Minority Oversampling for Long-tailed Classification](https://mlsanity.com/paper/2112.00412/) (2021)
- [MetaSAug: Meta Semantic Augmentation for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2103.12579/) (2021)
- [Recovery Guarantees for One-hidden-layer Neural Networks](https://mlsanity.com/paper/1706.03175/) (2017)
- [Shift: A Zero FLOP, Zero Parameter Alternative to Spatial Convolutions](https://mlsanity.com/paper/1711.08141/) (2017)
- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)

## Built on by (most cited first, 6 of 6)

- [A Provably Effective Method for Pruning Experts in Fine-tuned Sparse Mixture-of-Experts](https://mlsanity.com/paper/2405.16646/) (2024)
- [What Improves the Generalization of Graph Transformers? A Theoretical Dive into the Self-attention and Positional Encoding](https://mlsanity.com/paper/2406.01977/) (2024)
- [Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis](https://mlsanity.com/paper/2406.17167/) (2024)
- [How Can Mamba Learn In Context with Outliers and Generalize Provably?](https://mlsanity.com/paper/2510.00399/) (2025)
- [FairNet: Dynamic Fairness Correction without Performance Loss via Contrastive Conditional LoRA](https://mlsanity.com/paper/2510.19421/) (2025)
- [Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification](https://mlsanity.com/paper/2507.05533/) (2025)

## Abstract (arXiv)

Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy, a theoretical generalization analysis of ERM on individual groups remains elusive. By formulating the group imbalance problem with the Gaussian Mixture Model, this paper quantifies the impact of individual groups on the sample complexity, the convergence rate, and the average and group-level testing performance. Although our theoretical framework is centered on binary classification using a one-hidden-layer neural network, to the best of our knowledge, we provide the first theoretical analysis of the group-level generalization of ERM in addition to the commonly studied average generalization performance. Sample insights of our theoretical results include that when all group-level co-variance is in the medium regime and all mean are close to zero, the learning performance is most desirable in the sense of a small sample complexity, a fast training rate, and a high average and group-level testing accuracy. Moreover, we show that increasing the fraction of the minority group in the training data does not necessarily improve the generalization performance of the minority group. Our theoretical results are validated on both synthetic and empirical datasets, such as CelebA and CIFAR-10 in image classification.