# Bilateral Sharpness-Aware Minimization for Flatter Minima

arXiv: https://arxiv.org/abs/2409.13173 · HTML: https://mlsanity.com/paper/2409.13173/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [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)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (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)
- [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)
- [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)
- [Fisher SAM: Information Geometry and Sharpness Aware Minimisation](https://mlsanity.com/paper/2206.04920/) (2022)
- [Regularizing Neural Networks via Adversarial Model Perturbation](https://mlsanity.com/paper/2010.04925/) (2020)
- [SimCC: a Simple Coordinate Classification Perspective for Human Pose Estimation](https://mlsanity.com/paper/2107.03332/) (2021)
- [On the Maximum Hessian Eigenvalue and Generalization](https://mlsanity.com/paper/2206.10654/) (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)

## Built on by (most cited first, 2 of 2)

- [NCSAM Noise-Compensated Sharpness-Aware Minimization for Noisy Label Learning](https://mlsanity.com/paper/2601.19947/) (2026)
- [Gradient-Energy Guided Block-Wise Perturbations for Sharpness-Aware Minimization](https://mlsanity.com/paper/2607.18306/) (2026)

## Abstract (arXiv)

Sharpness-Aware Minimization (SAM) enhances generalization by reducing a Max-Sharpness (MaxS). Despite the practical success, we empirically found that the MAxS behind SAM's generalization enhancements face the "Flatness Indicator Problem" (FIP), where SAM only considers the flatness in the direction of gradient ascent, resulting in a next minimization region that is not sufficiently flat. A better Flatness Indicator (FI) would bring a better generalization of neural networks. Because SAM is a greedy search method in nature. In this paper, we propose to utilize the difference between the training loss and the minimum loss over the neighborhood surrounding the current weight, which we denote as Min-Sharpness (MinS). By merging MaxS and MinS, we created a better FI that indicates a flatter direction during the optimization. Specially, we combine this FI with SAM into the proposed Bilateral SAM (BSAM) which finds a more flatter minimum than that of SAM. The theoretical analysis proves that BSAM converges to local minima. Extensive experiments demonstrate that BSAM offers superior generalization performance and robustness compared to vanilla SAM across various tasks, i.e., classification, transfer learning, human pose estimation, and network quantization. Code is publicly available at: https://github.com/ajiaaa/BSAM.