# Make Sharpness-Aware Minimization Stronger: A Sparsified Perturbation Approach

arXiv: https://arxiv.org/abs/2210.05177 · HTML: https://mlsanity.com/paper/2210.05177/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 64 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (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)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [Sparse Networks from Scratch: Faster Training without Losing Performance](https://mlsanity.com/paper/1907.04840/) (2019)

## Built on by (most cited first, 30 of 70)

- [Vaccine: Perturbation-aware Alignment for Large Language Models against Harmful Fine-tuning Attack](https://mlsanity.com/paper/2402.01109/) (2024)
- [Enhancing Fine-Tuning Based Backdoor Defense with Sharpness-Aware Minimization](https://mlsanity.com/paper/2304.11823/) (2023)
- [Gradient Norm Aware Minimization Seeks First-Order Flatness and Improves Generalization](https://mlsanity.com/paper/2303.03108/) (2023)
- [Friendly Sharpness-Aware Minimization](https://mlsanity.com/paper/2403.12350/) (2024)
- [FedSpeed: Larger Local Interval, Less Communication Round, and Higher Generalization Accuracy](https://mlsanity.com/paper/2302.10429/) (2023)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [Improving the Model Consistency of Decentralized Federated Learning](https://mlsanity.com/paper/2302.04083/) (2023)
- [Enhancing Sharpness-Aware Optimization Through Variance Suppression](https://mlsanity.com/paper/2309.15639/) (2023)
- [Make Landscape Flatter in Differentially Private Federated Learning](https://mlsanity.com/paper/2303.11242/) (2023)
- [The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training](https://mlsanity.com/paper/2502.19002/) (2025)
- [Robust Generalization against Photon-Limited Corruptions via Worst-Case Sharpness Minimization](https://mlsanity.com/paper/2303.13087/) (2023)
- [Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization](https://mlsanity.com/paper/2405.18890/) (2024)
- [Normalization Layers Are All That Sharpness-Aware Minimization Needs](https://mlsanity.com/paper/2306.04226/) (2023)
- [Flatness-Aware Minimization for Domain Generalization](https://mlsanity.com/paper/2307.11108/) (2023)
- [The Crucial Role of Normalization in Sharpness-Aware Minimization](https://mlsanity.com/paper/2305.15287/) (2023)
- [On the Duality Between Sharpness-Aware Minimization and Adversarial Training](https://mlsanity.com/paper/2402.15152/) (2024)
- [AdaSAM: Boosting Sharpness-Aware Minimization with Adaptive Learning Rate and Momentum for Training Deep Neural Networks](https://mlsanity.com/paper/2303.00565/) (2023)
- [Practical Sharpness-Aware Minimization Cannot Converge All the Way to Optima](https://mlsanity.com/paper/2306.09850/) (2023)
- [Mitigating Parameter Interference in Model Merging via Sharpness-Aware Fine-Tuning](https://mlsanity.com/paper/2504.14662/) (2025)
- [Decentralized SGD and Average-direction SAM are Asymptotically Equivalent](https://mlsanity.com/paper/2306.02913/) (2023)
- [Improving Visual Prompt Tuning by Gaussian Neighborhood Minimization for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2410.21042/) (2024)
- [Sharpness-Aware Minimization Alone can Improve Adversarial Robustness](https://mlsanity.com/paper/2305.05392/) (2023)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Momentum-SAM: Sharpness Aware Minimization without Computational Overhead](https://mlsanity.com/paper/2401.12033/) (2024)
- [Improving Generalization and Convergence by Enhancing Implicit Regularization](https://mlsanity.com/paper/2405.20763/) (2024)
- [A Universal Class of Sharpness-Aware Minimization Algorithms](https://mlsanity.com/paper/2406.03682/) (2024)
- [Revisiting Random Weight Perturbation for Efficiently Improving Generalization](https://mlsanity.com/paper/2404.00357/) (2024)
- [Domain-Inspired Sharpness-Aware Minimization Under Domain Shifts](https://mlsanity.com/paper/2405.18861/) (2024)
- [CR-SAM: Curvature Regularized Sharpness-Aware Minimization](https://mlsanity.com/paper/2312.13555/) (2023)
- [Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems](https://mlsanity.com/paper/2410.14802/) (2024)

## Abstract (arXiv)

Deep neural networks often suffer from poor generalization caused by complex and non-convex loss landscapes. One of the popular solutions is Sharpness-Aware Minimization (SAM), which smooths the loss landscape via minimizing the maximized change of training loss when adding a perturbation to the weight. However, we find the indiscriminate perturbation of SAM on all parameters is suboptimal, which also results in excessive computation, i.e., double the overhead of common optimizers like Stochastic Gradient Descent (SGD). In this paper, we propose an efficient and effective training scheme coined as Sparse SAM (SSAM), which achieves sparse perturbation by a binary mask. To obtain the sparse mask, we provide two solutions which are based onFisher information and dynamic sparse training, respectively. In addition, we theoretically prove that SSAM can converge at the same rate as SAM, i.e., O(log T/√T). Sparse SAM not only has the potential for training acceleration but also smooths the loss landscape effectively. Extensive experimental results on CIFAR10, CIFAR100, and ImageNet-1K confirm the superior efficiency of our method to SAM, and the performance is preserved or even better with a perturbation of merely 50% sparsity. Code is availiable at https://github.com/Mi-Peng/Sparse-Sharpness-Aware-Minimization.