# Gradient-Energy Guided Block-Wise Perturbations for Sharpness-Aware Minimization

arXiv: https://arxiv.org/abs/2607.18306 · HTML: https://mlsanity.com/paper/2607.18306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 31 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [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)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [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)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)
- [Fisher SAM: Information Geometry and Sharpness Aware Minimisation](https://mlsanity.com/paper/2206.04920/) (2022)
- [Make Sharpness-Aware Minimization Stronger: A Sparsified Perturbation Approach](https://mlsanity.com/paper/2210.05177/) (2022)
- [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)
- [An Adaptive Policy to Employ Sharpness-Aware Minimization](https://mlsanity.com/paper/2304.14647/) (2023)
- [Improving Sharpness-Aware Minimization with Fisher Mask for Better Generalization on Language Models](https://mlsanity.com/paper/2210.05497/) (2022)
- [Normalization Layers Are All That Sharpness-Aware Minimization Needs](https://mlsanity.com/paper/2306.04226/) (2023)
- [The Crucial Role of Normalization in Sharpness-Aware Minimization](https://mlsanity.com/paper/2305.15287/) (2023)
- [FAdam: Adam is a natural gradient optimizer using diagonal empirical Fisher information](https://mlsanity.com/paper/2405.12807/) (2024)
- [Sharpness-Aware Minimization and the Edge of Stability](https://mlsanity.com/paper/2309.12488/) (2023)
- [K-SAM: Sharpness-Aware Minimization at the Speed of SGD](https://mlsanity.com/paper/2210.12864/) (2022)
- [CR-SAM: Curvature Regularized Sharpness-Aware Minimization](https://mlsanity.com/paper/2312.13555/) (2023)
- [μP2: Effective Sharpness Aware Minimization Requires Layerwise Perturbation Scaling](https://mlsanity.com/paper/2411.00075/) (2024)
- [SAMPa: Sharpness-aware Minimization Parallelized](https://mlsanity.com/paper/2410.10683/) (2024)
- [Layer-wise Adaptive Gradient Norm Penalizing Method for Efficient and Accurate Deep Learning](https://mlsanity.com/paper/2503.14205/) (2025)
- [Bilateral Sharpness-Aware Minimization for Flatter Minima](https://mlsanity.com/paper/2409.13173/) (2024)
- [Sparse Layer Sharpness-Aware Minimization for Efficient Fine-Tuning](https://mlsanity.com/paper/2602.09395/) (2026)

## Abstract (arXiv)

Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss in a local parameter neighborhood. Standard SAM implicitly allocates its global perturbation budget across parameter blocks according to instantaneous minibatch gradient norms. Such an allocation can be noisy and may not reflect the sensitivity that blocks accumulate throughout training. We propose Gradient-Energy Adaptive Radius SAM (GEAR-SAM), which maintains an exponential moving average (EMA) of squared block gradients as a lightweight, curvature-related sensitivity signal and allocates the fixed SAM budget through a closed-form constrained optimization. GEAR-SAM preserves the global SAM radius, requires no Hessian-vector products or explicit Fisher estimation, and adds only scalar state beyond SAM. Experiments on image classification, transfer learning, noisy-label learning, and partition studies demonstrate improved generalization and robustness across architectures and tasks. More broadly, GEAR-SAM provides a dynamic view of sharpness-aware optimization: a fixed perturbation budget should be redistributed as the sensitivity of functional network blocks evolves during training.