Efficient Sharpness-aware Minimization for Improved Training of Neural Networks
Not on the map. Why?
Abstract (arXiv)
Overparametrized Deep Neural Networks (DNNs) often achieve astounding performances, but may potentially result in severe generalization error. Recently, the relation between the sharpness of the loss landscape and the generalization error has been established by Foret et al. (2020), in which the Sharpness Aware Minimizer (SAM) was proposed to mitigate the degradation of the generalization. Unfortunately, SAM s computational cost is roughly double that of base optimizers, such as Stochastic Gradient Descent (SGD). This paper thus proposes Efficient Sharpness Aware Minimizer (ESAM), which boosts SAM s efficiency at no cost to its generalization performance. ESAM includes two novel and efficient training strategies-StochasticWeight Perturbation and Sharpness-Sensitive Data Selection. In the former, the sharpness measure is approximated by perturbing a stochastically chosen set of weights in each iteration; in the latter, the SAM loss is optimized using only a judiciously selected subset of data that is sensitive to the sharpness. We provide theoretical explanations as to why these strategies perform well. We also show, via extensive experiments on the CIFAR and ImageNet datasets, that ESAM enhances the efficiency over SAM from requiring 100% extra computations to 40% vis-a-vis base optimizers, while test accuracies are preserved or even improved.
Key facts. Cited by 137 papers in the map (data through 7 Oct 2026). Builds on 31 of its 39 references that are in the map. First posted on arXiv 7 Oct 2021.
Builds on
31 of 39 references.
References · 31
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
- 2021Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervisioncited by 3,848
- 2016Wide Residual Networkscited by 3,057
- 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,404
- 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
- 2017Visualizing the Loss Landscape of Neural Netscited by 1,126
- 2017Exploring Generalization in Deep Learningcited by 595
- 2017Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Datacited by 527
- 2019Fantastic Generalization Measures and Where to Find Themcited by 507
- 2017Sharp Minima Can Generalize For Deep Netscited by 462
19 more
- 2020Meta Pseudo Labelscited by 372
- 2016Entropy-SGD: Biasing Gradient Descent Into Wide Valleyscited by 357
- 2019Lookahead Optimizer: k steps forward, 1 step backcited by 333
- 2021ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networkscited by 293
- 2021When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentationscited by 259
- 2018Robustness via curvature regularization, and vice versacited by 174
- 2021VOLO: Vision Outlooker for Visual Recognitioncited by 164
- 2016Deep Pyramidal Residual Networkscited by 163
- 2019Adversarial Robustness through Local Linearizationcited by 146
- 2021Label Noise SGD Provably Prefers Flat Global Minimizerscited by 121
- 2018Gradient Harmonized Single-stage Detectorcited by 114
- 2019On Robustness of Neural Ordinary Differential Equationscited by 83
- 2020Regularizing Neural Networks via Adversarial Model Perturbationcited by 78
- 2020On the Loss Landscape of Adversarial Training: Identifying Challenges and How to Overcome Themcited by 59
- 2019Query-efficient Meta Attack to Deep Neural Networkscited by 33
- 2021Scaled ReLU Matters for Training Vision Transformerscited by 29
- 2021CIFS: Improving Adversarial Robustness of CNNs via Channel-wise Importance-based Feature Selectioncited by 21
- 2021UPANets: Learning from the Universal Pixel Attention Networkscited by 7
- 2021Using Early-Learning Regularization to Classify Real-World Noisy Datacited by 1
Built on by
Citing papers per year: 2021: 2; 2022: 23; 2023: 40; 2024: 34; 2025: 26; 2026: 12.
137 papers.
Sort:
By area:
- 2023Towards Stable Test-Time Adaptation in Dynamic Wild Worldcited by 409
- 2022Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Modelscited by 172
- 2022Generalized Federated Learning via Sharpness Aware Minimizationcited by 144
- 2022Minimizing the Accumulated Trajectory Error to Improve Dataset Distillationcited by 142
- 2022Towards Efficient and Scalable Sharpness-Aware Minimizationcited by 129
- 2023Sharpness-Aware Gradient Matching for Domain Generalizationcited by 102
- 2022Sharpness-Aware Training for Freecited by 95
- 2022Make Sharpness-Aware Minimization Stronger: A Sparsified Perturbation Approachcited by 70
- 2022Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learningcited by 57
- 2023Revisiting Weighted Aggregation in Federated Learning with Neural Networkscited by 57
- 2023Gradient Norm Aware Minimization Seeks First-Order Flatness and Improves Generalizationcited by 57
- 2024Friendly Sharpness-Aware Minimizationcited by 52
38 more
- 2022The Dynamics of Sharpness-Aware Minimization: Bouncing Across Ravines and Drifting Towards Wide Minimacited by 51
- 2023Improving the Model Consistency of Decentralized Federated Learningcited by 45
- 2023An Adaptive Policy to Employ Sharpness-Aware Minimizationcited by 43
- 2022Improving Sharpness-Aware Minimization with Fisher Mask for Better Generalization on Language Modelscited by 42
- 2022Compute-Efficient Deep Learning: Algorithmic Trends and Opportunitiescited by 38
- 2023Spanning Training Progress: Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruningcited by 38
- 2023A Survey on Efficient Training of Transformerscited by 37
- 2023Enhancing Sharpness-Aware Optimization Through Variance Suppressioncited by 37
- 2023Make Landscape Flatter in Differentially Private Federated Learningcited by 33
- 2023Why Does Little Robustness Help? A Further Step Towards Understanding Adversarial Transferabilitycited by 32
- 2023Robust Generalization against Photon-Limited Corruptions via Worst-Case Sharpness Minimizationcited by 29
- 2024Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimizationcited by 28
- 2023Normalization Layers Are All That Sharpness-Aware Minimization Needscited by 27
- 2023Flatness-Aware Minimization for Domain Generalizationcited by 27
- 2023The Crucial Role of Normalization in Sharpness-Aware Minimizationcited by 26
- 2024Gradient Alignment for Cross-Domain Face Anti-Spoofingcited by 26
- 2021Sharpness-aware Quantization for Deep Neural Networkscited by 25
- 2024On the Duality Between Sharpness-Aware Minimization and Adversarial Trainingcited by 24
- 2024Sharpness-Aware Minimization Efficiently Selects Flatter Minima Late in Trainingcited by 24
- 2023An SDE for Modeling SAM: Theory and Insightscited by 22
- 2023AdaSAM: Boosting Sharpness-Aware Minimization with Adaptive Learning Rate and Momentum for Training Deep Neural Networkscited by 21
- 2022Train Flat, Then Compress: Sharpness-Aware Minimization Learns More Compressible Modelscited by 20
- 2023Practical Sharpness-Aware Minimization Cannot Converge All the Way to Optimacited by 20
- 2023FlatMatch: Bridging Labeled Data and Unlabeled Data with Cross-Sharpness for Semi-Supervised Learningcited by 20
- 2022Bootstrap Generalization Ability from Loss Landscape Perspectivecited by 16
- 2023Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Termcited by 16
- 2022Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspectivecited by 15
- 2023Decentralized SGD and Average-direction SAM are Asymptotically Equivalentcited by 15
- 2022Randomized Sharpness-Aware Training for Boosting Computational Efficiency in Deep Learningcited by 14
- 2023Stability Analysis of Sharpness-Aware Minimizationcited by 14
- 2023Sharpness-Aware Minimization Alone can Improve Adversarial Robustnesscited by 14
- 2023Differentially Private Sharpness-Aware Trainingcited by 14
- 2024Improving Generalization and Convergence by Enhancing Implicit Regularizationcited by 14
- 2022GA-SAM: Gradient-Strength based Adaptive Sharpness-Aware Minimization for Improved Generalizationcited by 13
- 2024Momentum-SAM: Sharpness Aware Minimization without Computational Overheadcited by 13
- 2024Revisiting Random Weight Perturbation for Efficiently Improving Generalizationcited by 13
- 2023Chasing Fairness Under Distribution Shift: A Model Weight Perturbation Approachcited by 12
- 2024Domain-Inspired Sharpness-Aware Minimization Under Domain Shiftscited by 12
50 most cited of 137 All 137 (JSON)
- 2026Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm28 Jul 2026
- 2026Gradient-Energy Guided Block-Wise Perturbations for Sharpness-Aware Minimization17 Jul 2026
- 2026Why Muon Outperforms Adam: A Curvature Perspective3 Jun 2026
- 2026Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization11 May 2026
- 2026FedVSSAM: Mitigating Flatness Incompatibility in Sharpness-Aware Federated Learning9 May 2026
- 2026A Faster Path to Continual Learning13 Apr 2026
- 2026Sharpness Aware Surrogate Training for Spiking Neural Networks14 Mar 2026
- 2026ZO-SAM: Zero-Order Sharpness-Aware Minimization for Efficient Sparse Training13 Mar 2026
- 2026Revisiting Sharpness-Aware Minimization: A More Faithful and Effective Implementation9 Mar 2026
- 2026Sparse Layer Sharpness-Aware Minimization for Efficient Fine-Tuning10 Feb 2026
- 2026Incorruptible Neural Networks: Training Models that can Generalize to Large Internal Perturbations7 Feb 2026
- 2026Beyond Superficial Unlearning: Sharpness-Aware Robust Erasure of Hallucinations in Multimodal LLMs23 Jan 2026
38 more
- 2025Sharpness-aware Dynamic Anchor Selection for Generalized Category Discovery15 Dec 2025
- 2025A Unified Stability Analysis of SAM vs SGD: Role of Data Coherence and Emergence of Simplicity Bias21 Nov 2025
- 2025Flat Minima and Generalization: Insights from Stochastic Convex Optimization5 Nov 2025
- 2025Zeroth-Order Sharpness-Aware Learning with Exponential Tilting17 Oct 2025
- 2025Adjusting Initial Noise to Mitigate Memorization in Text-to-Image Diffusion Models8 Oct 2025
- 2025Sharpness-Aware Data Generation for Zero-shot Quantization8 Oct 2025
- 2025Adaptively Sampling-Reusing-Mixing Decomposed Gradients to Speed Up Sharpness Aware Minimization4 Oct 2025
- 2025Flatness-Aware Stochastic Gradient Langevin Dynamics2 Oct 2025
- 2025Beyond Magic Words: Sharpness-Aware Prompt Evolving for Robust Large Language Models with TARE28 Sep 2025
- 2025Sharpness-Aware Minimization Can Hallucinate Minimizers26 Sep 2025
- 2025Unveiling m-Sharpness Through the Structure of Stochastic Gradient Noise22 Sep 2025
- 2025Adapt in the Wild: Test-Time Entropy Minimization with Sharpness and Feature Regularization5 Sep 2025
- 2025LSAM: Asynchronous Distributed Training with Landscape-Smoothed Sharpness-Aware Minimization3 Sep 2025
- 2025VASSO: Variance Suppression for Sharpness-Aware Minimization2 Sep 2025
- 2025Bi-LoRA: Efficient Sharpness-Aware Minimization for Fine-Tuning Large-Scale Models27 Aug 2025
- 2025Unpacking the Implicit Norm Dynamics of Sharpness-Aware Minimization in Tensorized Models14 Aug 2025
- 2025Domain-Generalization to Improve Learning in Meta-Learning Algorithms13 Aug 2025
- 2025SAMO: A Lightweight Sharpness-Aware Approach for Multi-Task Optimization with Joint Global-Local Perturbation10 Jul 2025
- 2025Attributing Data for Sharpness-Aware Minimization5 Jul 2025
- 2025FEDTAIL: Federated Long-Tailed Domain Generalization with Sharpness-Guided Gradient Matching10 Jun 2025
- 2025Towards Understanding The Calibration Benefits of Sharpness-Aware Minimization29 May 2025
- 2025DGSAM: Domain Generalization via Individual Sharpness-Aware Minimization30 Mar 2025
- 2025EasyRobust: A Comprehensive and Easy-to-use Toolkit for Robust and Generalized Vision21 Mar 2025
- 2025Layer-wise Adaptive Gradient Norm Penalizing Method for Efficient and Accurate Deep Learning18 Mar 2025
- 2025SASSHA: Sharpness-aware Adaptive Second-order Optimization with Stable Hessian Approximation25 Feb 2025
- 2025GCSAM: Gradient Centralized Sharpness Aware Minimization20 Jan 2025
- 2024Sharpness-Aware Minimization with Adaptive Regularization for Training Deep Neural Networks22 Dec 2024
- 2024SSE-SAM: Balancing Head and Tail Classes Gradually through Stage-Wise SAM18 Dec 2024
- 2024The Impact of Generalization Techniques on the Interplay Among Privacy, Utility, and Fairness in Image Classification16 Dec 2024
- 2024Towards Understanding the Role of Sharpness-Aware Minimization Algorithms for Out-of-Distribution Generalization6 Dec 2024
- 2024Beyond Local Sharpness: Communication-Efficient Global Sharpness-aware Minimization for Federated Learning4 Dec 2024
- 2024Fast Graph Sharpness-Aware Minimization for Enhancing and Accelerating Few-Shot Node Classification22 Oct 2024
- 2024Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems18 Oct 2024
- 2024SAMPa: Sharpness-aware Minimization Parallelized14 Oct 2024
- 2024Sharpness-Aware Minimization Efficiently Selects Flatter Minima Late in Training14 Oct 2024
- 2024Bilateral Sharpness-Aware Minimization for Flatter Minima20 Sep 2024
- 2024Convergence of Sharpness-Aware Minimization Algorithms using Increasing Batch Size and Decaying Learning Rate16 Sep 2024
- 2024COSCO: A Sharpness-Aware Training Framework for Few-shot Multivariate Time Series Classification15 Sep 2024
50 newest of 137 All 137 (JSON)
- 2023Towards Stable Test-Time Adaptation in Dynamic Wild Worldcited by 409
- 2022Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Modelscited by 172
- 2022Generalized Federated Learning via Sharpness Aware Minimizationcited by 144
- 2022Minimizing the Accumulated Trajectory Error to Improve Dataset Distillationcited by 142
- 2022Towards Efficient and Scalable Sharpness-Aware Minimizationcited by 129
- 2023Sharpness-Aware Gradient Matching for Domain Generalizationcited by 102
- 2022Sharpness-Aware Training for Freecited by 95
- 2022Make Sharpness-Aware Minimization Stronger: A Sparsified Perturbation Approachcited by 70
- 2022Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learningcited by 57
- 2023Revisiting Weighted Aggregation in Federated Learning with Neural Networkscited by 57
- 2023Gradient Norm Aware Minimization Seeks First-Order Flatness and Improves Generalizationcited by 57
- 2024Friendly Sharpness-Aware Minimizationcited by 52
12 most cited of 135 All 135 (JSON)
- 2026Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm28 Jul 2026
- 2026Gradient-Energy Guided Block-Wise Perturbations for Sharpness-Aware Minimization17 Jul 2026
- 2026Why Muon Outperforms Adam: A Curvature Perspective3 Jun 2026
- 2026Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization11 May 2026
- 2026FedVSSAM: Mitigating Flatness Incompatibility in Sharpness-Aware Federated Learning9 May 2026
- 2026A Faster Path to Continual Learning13 Apr 2026
- 2026Sharpness Aware Surrogate Training for Spiking Neural Networks14 Mar 2026
- 2026ZO-SAM: Zero-Order Sharpness-Aware Minimization for Efficient Sparse Training13 Mar 2026
- 2026Revisiting Sharpness-Aware Minimization: A More Faithful and Effective Implementation9 Mar 2026
- 2026Sparse Layer Sharpness-Aware Minimization for Efficient Fine-Tuning10 Feb 2026
- 2026Incorruptible Neural Networks: Training Models that can Generalize to Large Internal Perturbations7 Feb 2026
- 2025Sharpness-aware Dynamic Anchor Selection for Generalized Category Discovery15 Dec 2025
12 newest of 135 All 135 (JSON)