# Sharpness-Aware Gradient Matching for Domain Generalization

arXiv: https://arxiv.org/abs/2303.10353 · HTML: https://mlsanity.com/paper/2303.10353/

## Key facts

- Cited by 102 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 57 references that are in the map.
- First posted on arXiv 18 Mar 2023.

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

- [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)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (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)
- [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)
- [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)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Adversarial Domain Adaptation with Domain Mixup](https://mlsanity.com/paper/1912.01805/) (2019)

## Built on by (most cited first, 30 of 102)

- [Leveraging Vision-Language Models for Improving Domain Generalization in Image Classification](https://mlsanity.com/paper/2310.08255/) (2023)
- [Enhancing Sharpness-Aware Optimization Through Variance Suppression](https://mlsanity.com/paper/2309.15639/) (2023)
- [GeneOH Diffusion: Towards Generalizable Hand-Object Interaction Denoising via Denoising Diffusion](https://mlsanity.com/paper/2402.14810/) (2024)
- [Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization](https://mlsanity.com/paper/2405.18890/) (2024)
- [Gradient Alignment for Cross-Domain Face Anti-Spoofing](https://mlsanity.com/paper/2402.18817/) (2024)
- [Fast-Slow Test-Time Adaptation for Online Vision-and-Language Navigation](https://mlsanity.com/paper/2311.13209/) (2023)
- [DGMamba: Domain Generalization via Generalized State Space Model](https://mlsanity.com/paper/2404.07794/) (2024)
- [Practical Sharpness-Aware Minimization Cannot Converge All the Way to Optima](https://mlsanity.com/paper/2306.09850/) (2023)
- [FlatMatch: Bridging Labeled Data and Unlabeled Data with Cross-Sharpness for Semi-Supervised Learning](https://mlsanity.com/paper/2310.16412/) (2023)
- [Learning to Unlearn while Retaining: Combating Gradient Conflicts in Machine Unlearning](https://mlsanity.com/paper/2503.06339/) (2025)
- [Mitigating Parameter Interference in Model Merging via Sharpness-Aware Fine-Tuning](https://mlsanity.com/paper/2504.14662/) (2025)
- [PracticalDG: Perturbation Distillation on Vision-Language Models for Hybrid Domain Generalization](https://mlsanity.com/paper/2404.09011/) (2024)
- [CLIP-Powered Domain Generalization and Domain Adaptation: A Comprehensive Survey](https://mlsanity.com/paper/2504.14280/) (2025)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Domain Generalisation via Risk Distribution Matching](https://mlsanity.com/paper/2310.18598/) (2023)
- [A Universal Class of Sharpness-Aware Minimization Algorithms](https://mlsanity.com/paper/2406.03682/) (2024)
- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [Domain-Inspired Sharpness-Aware Minimization Under Domain Shifts](https://mlsanity.com/paper/2405.18861/) (2024)
- [Gradient Alignment Improves Test-Time Adaptation for Medical Image Segmentation](https://mlsanity.com/paper/2408.07343/) (2024)
- [Diverse Target and Contribution Scheduling for Domain Generalization](https://mlsanity.com/paper/2309.16460/) (2023)
- [Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems](https://mlsanity.com/paper/2410.14802/) (2024)
- [Seeking Consistent Flat Minima for Better Domain Generalization via Refining Loss Landscapes](https://mlsanity.com/paper/2412.13573/) (2024)
- [Sharpness-Aware Minimization Enhances Feature Quality via Balanced Learning](https://mlsanity.com/paper/2405.20439/) (2024)
- [Is Large-Scale Pretraining the Secret to Good Domain Generalization?](https://mlsanity.com/paper/2412.02856/) (2024)
- [Gradient-Guided Annealing for Domain Generalization](https://mlsanity.com/paper/2502.20162/) (2025)
- [NormAUG: Normalization-guided Augmentation for Domain Generalization](https://mlsanity.com/paper/2307.13492/) (2023)
- [HCVP: Leveraging Hierarchical Contrastive Visual Prompt for Domain Generalization](https://mlsanity.com/paper/2401.09716/) (2024)
- [Enhancing Domain Adaptation through Prompt Gradient Alignment](https://mlsanity.com/paper/2406.09353/) (2024)
- [Prompt Disentanglement via Language Guidance and Representation Alignment for Domain Generalization](https://mlsanity.com/paper/2507.02288/) (2025)
- [Generalizing to Unseen Domains in Diabetic Retinopathy Classification](https://mlsanity.com/paper/2310.17255/) (2023)

## Abstract (arXiv)

The goal of domain generalization (DG) is to enhance the generalization capability of the model learned from a source domain to other unseen domains. The recently developed Sharpness-Aware Minimization (SAM) method aims to achieve this goal by minimizing the sharpness measure of the loss landscape. Though SAM and its variants have demonstrated impressive DG performance, they may not always converge to the desired flat region with a small loss value. In this paper, we present two conditions to ensure that the model could converge to a flat minimum with a small loss, and present an algorithm, named Sharpness-Aware Gradient Matching (SAGM), to meet the two conditions for improving model generalization capability. Specifically, the optimization objective of SAGM will simultaneously minimize the empirical risk, the perturbed loss (i.e., the maximum loss within a neighborhood in the parameter space), and the gap between them. By implicitly aligning the gradient directions between the empirical risk and the perturbed loss, SAGM improves the generalization capability over SAM and its variants without increasing the computational cost. Extensive experimental results show that our proposed SAGM method consistently outperforms the state-of-the-art methods on five DG benchmarks, including PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet. Codes are available at https://github.com/Wang-pengfei/SAGM.