# Adversarial Data Augmentation for Single Domain Generalization via Lyapunov Exponent-Guided Optimization

arXiv: https://arxiv.org/abs/2507.04302 · HTML: https://mlsanity.com/paper/2507.04302/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 6 Jul 2025.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [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)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Learning to Diversify for Single Domain Generalization](https://mlsanity.com/paper/2108.11726/) (2021)
- [Robust and Generalizable Visual Representation Learning via Random Convolutions](https://mlsanity.com/paper/2007.13003/) (2020)
- [Deep Learning for Hyperspectral Image Classification: An Overview](https://mlsanity.com/paper/1910.12861/) (2019)
- [Maximum-Entropy Adversarial Data Augmentation for Improved Generalization and Robustness](https://mlsanity.com/paper/2010.08001/) (2020)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [Progressive Domain Expansion Network for Single Domain Generalization](https://mlsanity.com/paper/2103.16050/) (2021)
- [Deep Learning via Dynamical Systems: An Approximation Perspective](https://mlsanity.com/paper/1912.10382/) (2019)
- [MixStyle Neural Networks for Domain Generalization and Adaptation](https://mlsanity.com/paper/2107.02053/) (2021)
- [Attention Consistency on Visual Corruptions for Single-Source Domain Generalization](https://mlsanity.com/paper/2204.13091/) (2022)
- [On Lyapunov Exponents for RNNs: Understanding Information Propagation Using Dynamical Systems Tools](https://mlsanity.com/paper/2006.14123/) (2020)
- [Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective](https://mlsanity.com/paper/1908.10920/) (2019)
- [Flatness-Aware Minimization for Domain Generalization](https://mlsanity.com/paper/2307.11108/) (2023)

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

- [PhaseAT: Fourier Phase Adversarial Training for Medical Image Domain Generalization](https://mlsanity.com/paper/2610.01807/) (2026)

## Abstract (arXiv)

Single Domain Generalization (SDG) aims to develop models capable of generalizing to unseen target domains using only one source domain, a task complicated by substantial domain shifts and limited data diversity. Existing SDG approaches primarily rely on data augmentation techniques, which struggle to effectively adapt training dynamics to accommodate large domain shifts. To address this, we propose LEAwareSGD, a novel Lyapunov Exponent (LE)-guided optimization approach inspired by dynamical systems theory. By leveraging LE measurements to modulate the learning rate, LEAwareSGD encourages model training near the edge of chaos, a critical state that optimally balances stability and adaptability. This dynamic adjustment allows the model to explore a wider parameter space and capture more generalizable features, ultimately enhancing the model's generalization capability. Extensive experiments on PACS, OfficeHome, and DomainNet demonstrate that LEAwareSGD yields substantial generalization gains, achieving up to 9.47% improvement on PACS in low-data regimes. These results underscore the effectiveness of training near the edge of chaos for enhancing model generalization capability in SDG tasks.