# Improving Mixup Calibration with Wasserstein Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2506.17874 · HTML: https://mlsanity.com/paper/2506.17874/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Listen, Attend and Spell](https://mlsanity.com/paper/1508.01211/) (2015)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [How Does Mixup Help With Robustness and Generalization?](https://mlsanity.com/paper/2010.04819/) (2020)
- [Improving the Robustness of Deep Neural Networks via Stability Training](https://mlsanity.com/paper/1604.04326/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [Motivating the Rules of the Game for Adversarial Example Research](https://mlsanity.com/paper/1807.06732/) (2018)
- [Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations](https://mlsanity.com/paper/2206.09527/) (2022)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)
- [NoisyMix: Boosting Model Robustness to Common Corruptions](https://mlsanity.com/paper/2202.01263/) (2022)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension](https://mlsanity.com/paper/2302.05851/) (2023)
- [Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity](https://mlsanity.com/paper/2005.13815/) (2020)
- [What Are Effective Labels for Augmented Data? Improving Calibration and Robustness with AutoLabel](https://mlsanity.com/paper/2302.11188/) (2023)
- [Tailoring Mixup to Data for Calibration](https://mlsanity.com/paper/2311.01434/) (2023)
- [Distributionally Robust Multiclass Classification and Applications in Deep Image Classifiers](https://mlsanity.com/paper/2109.12772/) (2021)

## Built on by (most cited first, 1 of 1)

- [Unification and Optimization of Robust Supervised Learning](https://mlsanity.com/paper/2605.28165/) (2026)

## Abstract (arXiv)

In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While Mixup-based data augmentation techniques have been widely adopted to enhance the resilience of trained models against such perturbations, our experiments reveal an important corruption robustness-calibration trade-off: stronger Mixup-based augmentation can improve robustness against corrupted data while substantially increasing expected calibration error (ECE). To address this challenge, we introduce DRO-Augment, a framework that integrates Wasserstein Distributionally Robust Optimization (W-DRO) with various Mixup-based data augmentation strategies to mitigate this trade-off. Our method substantially reduces ECE under strong Mixup-based augmentation while largely preserving corruption accuracy across CIFAR-10, CIFAR-100, CIFAR-10-C, and CIFAR-100-C. On the theoretical side, we establish novel generalization error bounds for neural networks trained using a variation-regularized loss function with augmented data, closely related to the W-DRO problem. Furthermore, we introduce a refined CIFAR-C benchmark that corrects inconsistencies in corruption intensities, providing a more reliable evaluation for future robustness research.