# Momentum-SAM: Sharpness Aware Minimization without Computational Overhead

arXiv: https://arxiv.org/abs/2401.12033 · HTML: https://mlsanity.com/paper/2401.12033/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 59 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Don't Use Large Mini-Batches, Use Local SGD](https://mlsanity.com/paper/1808.07217/) (2018)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Towards Understanding Sharpness-Aware Minimization](https://mlsanity.com/paper/2206.06232/) (2022)
- [Efficient Sharpness-aware Minimization for Improved Training of Neural Networks](https://mlsanity.com/paper/2110.03141/) (2021)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)
- [Label Noise SGD Provably Prefers Flat Global Minimizers](https://mlsanity.com/paper/2106.06530/) (2021)
- [Sharpness-Aware Minimization Improves Language Model Generalization](https://mlsanity.com/paper/2110.08529/) (2021)
- [Better plain ViT baselines for ImageNet-1k](https://mlsanity.com/paper/2205.01580/) (2022)
- [Sharpness-Aware Training for Free](https://mlsanity.com/paper/2205.14083/) (2022)
- [A Modern Look at the Relationship between Sharpness and Generalization](https://mlsanity.com/paper/2302.07011/) (2023)

## Built on by (most cited first, 14 of 14)

- [Sharpness-Aware Minimization Efficiently Selects Flatter Minima Late in Training](https://mlsanity.com/paper/2410.10373/) (2024)
- [Training Dynamics of the Cooldown Stage in Warmup-Stable-Decay Learning Rate Scheduler](https://mlsanity.com/paper/2508.01483/) (2025)
- [LoRA-MGPO: Mitigating Double Descent in Low-Rank Adaptation via Momentum-Guided Perturbation Optimization](https://mlsanity.com/paper/2502.14538/) (2025)
- [Asymptotic Unbiased Sample Sampling to Speed Up Sharpness-Aware Minimization](https://mlsanity.com/paper/2406.08001/) (2024)
- [SASSHA: Sharpness-aware Adaptive Second-order Optimization with Stable Hessian Approximation](https://mlsanity.com/paper/2502.18153/) (2025)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [Bilateral Sharpness-Aware Minimization for Flatter Minima](https://mlsanity.com/paper/2409.13173/) (2024)
- [FairSAM: Fair Classification on Corrupted Image Data Through Sharpness-Aware Minimization](https://mlsanity.com/paper/2503.22934/) (2025)
- [CurvaDion: Curvature-Adaptive Distributed Orthonormalization](https://mlsanity.com/paper/2512.13728/) (2025)
- [Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization](https://mlsanity.com/paper/2605.10183/) (2026)
- [Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm](https://mlsanity.com/paper/2607.26001/) (2026)
- [Neighborhood and Global Perturbations Supported SAM in Federated Learning: From Local Tweaks To Global Awareness](https://mlsanity.com/paper/2408.14144/) (2024)
- [Sharpness-aware Federated Graph Learning](https://mlsanity.com/paper/2512.16247/) (2025)
- [EMASAM: a Computationally Efficient Sharpness-Aware Minimization via EMA-Guided Perturbations](https://mlsanity.com/paper/2608.15105/) (2026)

## Abstract (arXiv)

The recently proposed optimization algorithm for deep neural networks Sharpness Aware Minimization (SAM) suggests perturbing parameters before gradient calculation by a gradient ascent step to guide the optimization into parameter space regions of flat loss. While significant generalization improvements and thus reduction of overfitting could be demonstrated, the computational costs are doubled due to the additionally needed gradient calculation, making SAM unfeasible in case of limited computationally capacities. Motivated by Nesterov Accelerated Gradient (NAG) we propose Momentum-SAM (MSAM), which perturbs parameters in the direction of the accumulated momentum vector to achieve low sharpness without significant computational overhead or memory demands over SGD or Adam. We evaluate MSAM in detail and reveal insights on separable mechanisms of NAG, SAM and MSAM regarding training optimization and generalization. Code is available at https://github.com/MarlonBecker/MSAM.