# Seeking Consistent Flat Minima for Better Domain Generalization via Refining Loss Landscapes

arXiv: https://arxiv.org/abs/2412.13573 · HTML: https://mlsanity.com/paper/2412.13573/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 87 of its 113 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 30 of 87)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [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)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [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)
- [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)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (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)

## Built on by (most cited first, 10 of 10)

- [Modality-Balanced Collaborative Distillation for Multi-Modal Domain Generalization](https://mlsanity.com/paper/2511.20258/) (2025)
- [Harmonizing and Merging Source Models for CLIP-based Domain Generalization](https://mlsanity.com/paper/2506.09446/) (2025)
- [Sparsity-Driven Plasticity in Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2508.06871/) (2025)
- [Flatness Guided Test-Time Adaptation for Vision-Language Models](https://mlsanity.com/paper/2501.18864/) (2025)
- [Higher-Order Domain Generalization in Magnetic Resonance-Based Assessment of Alzheimer's Disease](https://mlsanity.com/paper/2601.01485/) (2026)
- [Ethical Fairness in Ubiquitous Health Sensing without Known Attributes](https://mlsanity.com/paper/2603.13373/) (2026)
- [TuneAhead: Predicting Fine-tuning Performance Before Full Training Begins](https://mlsanity.com/paper/2606.17660/) (2026)
- [A Unified Perspective on Optimization in Machine Learning and Neuroscience: From Gradient Descent to Neural Adaptation](https://mlsanity.com/paper/2510.18812/) (2025)
- [Neural Network Quantization by Learning Low-Loss Subspaces](https://mlsanity.com/paper/2606.25087/) (2026)
- [PAPT++: Risk-Aware Adversarial Tuning and Generation for Single Domain Generalization](https://mlsanity.com/paper/2609.04837/) (2026)

## Abstract (arXiv)

Domain generalization aims to learn a model from multiple training domains and generalize it to unseen test domains. Recent theory has shown that seeking the deep models, whose parameters lie in the flat minima of the loss landscape, can significantly reduce the out-of-domain generalization error. However, existing methods often neglect the consistency of loss landscapes in different domains, resulting in models that are not simultaneously in the optimal flat minima in all domains, which limits their generalization ability. To address this issue, this paper proposes an iterative Self-Feedback Training (SFT) framework to seek consistent flat minima that are shared across different domains by progressively refining loss landscapes during training. It alternatively generates a feedback signal by measuring the inconsistency of loss landscapes in different domains and refines these loss landscapes for greater consistency using this feedback signal. Benefiting from the consistency of the flat minima within these refined loss landscapes, our SFT helps achieve better out-of-domain generalization. Extensive experiments on DomainBed demonstrate superior performances of SFT when compared to state-of-the-art sharpness-aware methods and other prevalent DG baselines. On average across five DG benchmarks, SFT surpasses the sharpness-aware minimization by 2.6% with ResNet-50 and 1.5% with ViT-B/16, respectively. The code will be available soon.