# Adaptively Sampling-Reusing-Mixing Decomposed Gradients to Speed Up Sharpness Aware Minimization

arXiv: https://arxiv.org/abs/2510.03763 · HTML: https://mlsanity.com/paper/2510.03763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 4 Oct 2025.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (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)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (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)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Deep Pyramidal Residual Networks](https://mlsanity.com/paper/1610.02915/) (2016)
- [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)
- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)
- [Penalizing Gradient Norm for Efficiently Improving Generalization in Deep Learning](https://mlsanity.com/paper/2202.03599/) (2022)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [Sharpness-Aware Training for Free](https://mlsanity.com/paper/2205.14083/) (2022)
- [SimCC: a Simple Coordinate Classification Perspective for Human Pose Estimation](https://mlsanity.com/paper/2107.03332/) (2021)
- [On the Loss Landscape of Adversarial Training: Identifying Challenges and How to Overcome Them](https://mlsanity.com/paper/2006.08403/) (2020)
- [Gradient Norm Aware Minimization Seeks First-Order Flatness and Improves Generalization](https://mlsanity.com/paper/2303.03108/) (2023)

## Abstract (arXiv)

Sharpness-Aware Minimization (SAM) improves model generalization but doubles the computational cost of Stochastic Gradient Descent (SGD) by requiring twice the gradient calculations per optimization step. To mitigate this, we propose Adaptively sampling-Reusing-mixing decomposed gradients to significantly accelerate SAM (ARSAM). Concretely, we firstly discover that SAM's gradient can be decomposed into the SGD gradient and the Projection of the Second-order gradient onto the First-order gradient (PSF). Furthermore, we observe that the SGD gradient and PSF dynamically evolve during training, emphasizing the growing role of the PSF to achieve a flat minima. Therefore, ARSAM is proposed to the reused PSF and the timely updated PSF still maintain the model's generalization ability. Extensive experiments show that ARSAM achieves state-of-the-art accuracies comparable to SAM across diverse network architectures. On CIFAR-10/100, ARSAM is comparable to SAM while providing a speedup of about 40%. Moreover, ARSAM accelerates optimization for the various challenge tasks (textite.g., human pose estimation, and model quantization) without sacrificing performance, demonstrating its broad practicality.% The code is publicly accessible at: https://github.com/ajiaaa/ARSAM.