# Sharpness-Aware Minimization Leads to Low-Rank Features

arXiv: https://arxiv.org/abs/2305.16292 · HTML: https://mlsanity.com/paper/2305.16292/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 49 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 38)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [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)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [On Feature Decorrelation in Self-Supervised Learning](https://mlsanity.com/paper/2105.00470/) (2021)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [Towards Understanding Sharpness-Aware Minimization](https://mlsanity.com/paper/2206.06232/) (2022)
- [The Lazy Neuron Phenomenon: On Emergence of Activation Sparsity in Transformers](https://mlsanity.com/paper/2210.06313/) (2022)
- [Label Noise SGD Provably Prefers Flat Global Minimizers](https://mlsanity.com/paper/2106.06530/) (2021)
- [Regularizing Neural Networks via Adversarial Model Perturbation](https://mlsanity.com/paper/2010.04925/) (2020)

## Built on by (most cited first, 30 of 38)

- [Sharpness Minimization Algorithms Do Not Only Minimize Sharpness To Achieve Better Generalization](https://mlsanity.com/paper/2307.11007/) (2023)
- [Normalization Layers Are All That Sharpness-Aware Minimization Needs](https://mlsanity.com/paper/2306.04226/) (2023)
- [No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO](https://mlsanity.com/paper/2405.00662/) (2024)
- [Why is SAM Robust to Label Noise?](https://mlsanity.com/paper/2405.03676/) (2024)
- [Sharpness-Aware Minimization and the Edge of Stability](https://mlsanity.com/paper/2309.12488/) (2023)
- [Neural Collapse versus Low-rank Bias: Is Deep Neural Collapse Really Optimal?](https://mlsanity.com/paper/2405.14468/) (2024)
- [Decentralized SGD and Average-direction SAM are Asymptotically Equivalent](https://mlsanity.com/paper/2306.02913/) (2023)
- [Deep Grokking: Would Deep Neural Networks Generalize Better?](https://mlsanity.com/paper/2405.19454/) (2024)
- [Momentum-SAM: Sharpness Aware Minimization without Computational Overhead](https://mlsanity.com/paper/2401.12033/) (2024)
- [DeiT-LT Distillation Strikes Back for Vision Transformer Training on Long-Tailed Datasets](https://mlsanity.com/paper/2404.02900/) (2024)
- [A Universal Class of Sharpness-Aware Minimization Algorithms](https://mlsanity.com/paper/2406.03682/) (2024)
- [Sharpness-Aware Minimization: General Analysis and Improved Rates](https://mlsanity.com/paper/2503.02225/) (2025)
- [Sharpness-Aware Minimization Enhances Feature Quality via Balanced Learning](https://mlsanity.com/paper/2405.20439/) (2024)
- [A Theoretical Explanation of Activation Sparsity through Flat Minima and Adversarial Robustness](https://mlsanity.com/paper/2309.03004/) (2023)
- [Learning Low-Rank Feature for Thorax Disease Classification](https://mlsanity.com/paper/2404.18933/) (2024)
- [Simplicity Bias via Global Convergence of Sharpness Minimization](https://mlsanity.com/paper/2410.16401/) (2024)
- [Flat Minima and Generalization: Insights from Stochastic Convex Optimization](https://mlsanity.com/paper/2511.03548/) (2025)
- [Gradient Descent with Polyak's Momentum Finds Flatter Minima via Large Catapults](https://mlsanity.com/paper/2311.15051/) (2023)
- [Critical Influence of Overparameterization on Sharpness-aware Minimization](https://mlsanity.com/paper/2311.17539/) (2023)
- [Changing the Training Data Distribution to Reduce Simplicity Bias Improves In-distribution Generalization](https://mlsanity.com/paper/2404.17768/) (2024)
- [Towards Understanding the Role of Sharpness-Aware Minimization Algorithms for Out-of-Distribution Generalization](https://mlsanity.com/paper/2412.05169/) (2024)
- [Membership Privacy Risks of Sharpness Aware Minimization](https://mlsanity.com/paper/2310.00488/) (2023)
- [Towards Better Generalization: Weight Decay Induces Low-rank Bias for Neural Networks](https://mlsanity.com/paper/2410.02176/) (2024)
- [Attributing Data for Sharpness-Aware Minimization](https://mlsanity.com/paper/2507.04059/) (2025)
- [A Unified Stability Analysis of SAM vs SGD: Role of Data Coherence and Emergence of Simplicity Bias](https://mlsanity.com/paper/2511.17378/) (2025)
- [Overcoming Rank Collapse in Feedback Alignment](https://mlsanity.com/paper/2606.11123/) (2026)
- [RankFeat&RankWeight: Rank-1 Feature/Weight Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2311.13959/) (2023)
- [ATP: Enabling Fast LLM Serving via Attention on Top Principal Keys](https://mlsanity.com/paper/2403.02352/) (2024)
- [Convergence of Sharpness-Aware Minimization Algorithms using Increasing Batch Size and Decaying Learning Rate](https://mlsanity.com/paper/2409.09984/) (2024)
- [SAMO: A Lightweight Sharpness-Aware Approach for Multi-Task Optimization with Joint Global-Local Perturbation](https://mlsanity.com/paper/2507.07883/) (2025)

## Abstract (arXiv)

Sharpness-aware minimization (SAM) is a recently proposed method that minimizes the sharpness of the training loss of a neural network. While its generalization improvement is well-known and is the primary motivation, we uncover an additional intriguing effect of SAM: reduction of the feature rank which happens at different layers of a neural network. We show that this low-rank effect occurs very broadly: for different architectures such as fully-connected networks, convolutional networks, vision transformers and for different objectives such as regression, classification, language-image contrastive training. To better understand this phenomenon, we provide a mechanistic understanding of how low-rank features arise in a simple two-layer network. We observe that a significant number of activations gets entirely pruned by SAM which directly contributes to the rank reduction. We confirm this effect theoretically and check that it can also occur in deep networks, although the overall rank reduction mechanism can be more complex, especially for deep networks with pre-activation skip connections and self-attention layers. We make our code available at https://github.com/tml-epfl/sam-low-rank-features.