# Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term

arXiv: https://arxiv.org/abs/2305.15817 · HTML: https://mlsanity.com/paper/2305.15817/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 24 of 24)

- [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)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [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)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Efficient Sharpness-aware Minimization for Improved Training of Neural Networks](https://mlsanity.com/paper/2110.03141/) (2021)
- [Sharpness-Aware Minimization Improves Language Model Generalization](https://mlsanity.com/paper/2110.08529/) (2021)
- [Fisher SAM: Information Geometry and Sharpness Aware Minimisation](https://mlsanity.com/paper/2206.04920/) (2022)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)
- [Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning](https://mlsanity.com/paper/2206.03996/) (2022)
- [Understanding Generalization through Visualizations](https://mlsanity.com/paper/1906.03291/) (2019)

## Built on by (most cited first, 16 of 16)

- [A PAC-Bayesian Link Between Generalisation and Flat Minima](https://mlsanity.com/paper/2402.08508/) (2024)
- [Stabilizing Sharpness-aware Minimization Through A Simple Renormalization Strategy](https://mlsanity.com/paper/2401.07250/) (2024)
- [FlatNAS: optimizing Flatness in Neural Architecture Search for Out-of-Distribution Robustness](https://mlsanity.com/paper/2402.19102/) (2024)
- [LORENZA: Enhancing Generalization in Low-Rank Gradient LLM Training via Efficient Zeroth-Order Adaptive SAM](https://mlsanity.com/paper/2502.19571/) (2025)
- [Do Sharpness-based Optimizers Improve Generalization in Medical Image Analysis?](https://mlsanity.com/paper/2408.04065/) (2024)
- [Bi-LoRA: Efficient Sharpness-Aware Minimization for Fine-Tuning Large-Scale Models](https://mlsanity.com/paper/2508.19564/) (2025)
- [Towards Understanding The Calibration Benefits of Sharpness-Aware Minimization](https://mlsanity.com/paper/2505.23866/) (2025)
- [Model Merging via Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2512.21288/) (2025)
- [TimeCF: A TimeMixer-Based Model with adaptive Convolution and Sharpness-Aware Minimization Frequency Domain Loss for long-term time seris forecasting](https://mlsanity.com/paper/2505.17532/) (2025)
- [Towards Better Generalization via Distributional Input Projection Network](https://mlsanity.com/paper/2506.04690/) (2025)
- [Do Flat Minima Improve Sparse Novel View Synthesis?](https://mlsanity.com/paper/2511.17918/) (2025)
- [Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization](https://mlsanity.com/paper/2605.10183/) (2026)
- [LSAM: Asynchronous Distributed Training with Landscape-Smoothed Sharpness-Aware Minimization](https://mlsanity.com/paper/2509.03110/) (2025)
- [Sharpness-aware Federated Graph Learning](https://mlsanity.com/paper/2512.16247/) (2025)
- [X-SAM: Boosting Sharpness-Aware Minimization with Dominant-Eigenvector Gradient Correction](https://mlsanity.com/paper/2601.10251/) (2026)
- [Revisiting Sharpness-Aware Minimization: A More Faithful and Effective Implementation](https://mlsanity.com/paper/2603.10048/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNNs) generalization is known to be closely related to the flatness of minima, leading to the development of Sharpness-Aware Minimization (SAM) for seeking flatter minima and better generalization. In this paper, we revisit the loss of SAM and propose a more general method, called WSAM, by incorporating sharpness as a regularization term. We prove its generalization bound through the combination of PAC and Bayes-PAC techniques, and evaluate its performance on various public datasets. The results demonstrate that WSAM achieves improved generalization, or is at least highly competitive, compared to the vanilla optimizer, SAM and its variants. The code is available at https://github.com/intelligent-machine-learning/atorch/tree/main/atorch/optimizers.