# Learning Gradient-based Mixup with Extrapolation toward Flatter Minima for Domain Generalization

arXiv: https://arxiv.org/abs/2209.14742 · HTML: https://mlsanity.com/paper/2209.14742/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 56 references that are in the map.
- First posted on arXiv 29 Sep 2022.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [SelfReg: Self-supervised Contrastive Regularization for Domain Generalization](https://mlsanity.com/paper/2104.09841/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [Remix: Rebalanced Mixup](https://mlsanity.com/paper/2007.03943/) (2020)

## Built on by (most cited first, 2 of 2)

- [Incorporating Pre-training Data Matters in Unsupervised Domain Adaptation](https://mlsanity.com/paper/2308.03097/) (2023)
- [DGSAM: Domain Generalization via Individual Sharpness-Aware Minimization](https://mlsanity.com/paper/2503.23430/) (2025)

## Abstract (arXiv)

To address distribution shifts between training and test data, domain generalization (DG) leverages multiple source domains to learn a model that generalizes well to unseen domains. However, existing DG methods often overfit to the source domains, partly due to the limited coverage of the expected region in feature space. Motivated by this, we propose performing mixup with data interpolation and extrapolation to cover potentially unseen regions. To prevent the detrimental effects of unconstrained extrapolation, we carefully design a policy to generate the instance weights, named Flatness-aware Gradient-based Mixup (FGMix). The policy relies on gradient-based compatibilities to assign greater weights to instances that carry more invariant information and learn the mixup policy towards flatter minima for better generalization. On the DomainBed benchmark, we validate the efficacy of various designs of FGMix and demonstrate its superiority over other DG algorithms.