# Meta Curvature-Aware Minimization for Domain Generalization

arXiv: https://arxiv.org/abs/2412.11542 · HTML: https://mlsanity.com/paper/2412.11542/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 88 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 30 of 65)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (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)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [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)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [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)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [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)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)

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

- [MMRC: A Large-Scale Benchmark for Understanding Multimodal Large Language Model in Real-World Conversation](https://mlsanity.com/paper/2502.11903/) (2025)

## Abstract (arXiv)

Domain generalization (DG) aims to enhance the ability of models trained on source domains to generalize effectively to unseen domains. Recently, Sharpness-Aware Minimization (SAM) has shown promise in this area by reducing the sharpness of the loss landscape to obtain more generalized models. However, SAM and its variants sometimes fail to guide the model toward a flat minimum, and their training processes exhibit limitations, hindering further improvements in model generalization. In this paper, we first propose an improved model training process aimed at encouraging the model to converge to a flat minima. To achieve this, we design a curvature metric that has a minimal effect when the model is far from convergence but becomes increasingly influential in indicating the curvature of the minima as the model approaches a local minimum. Then we derive a novel algorithm from this metric, called Meta Curvature-Aware Minimization (MeCAM), to minimize the curvature around the local minima. Specifically, the optimization objective of MeCAM simultaneously minimizes the regular training loss, the surrogate gap of SAM, and the surrogate gap of meta-learning. We provide theoretical analysis on MeCAM's generalization error and convergence rate, and demonstrate its superiority over existing DG methods through extensive experiments on five benchmark DG datasets, including PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet. Code will be available on GitHub.