# Where Do Large Learning Rates Lead Us?

arXiv: https://arxiv.org/abs/2410.22113 · HTML: https://mlsanity.com/paper/2410.22113/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 71 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (2020)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)
- [The Break-Even Point on Optimization Trajectories of Deep Neural Networks](https://mlsanity.com/paper/2002.09572/) (2020)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [An Alternative View: When Does SGD Escape Local Minima?](https://mlsanity.com/paper/1802.06175/) (2018)
- [A Modern Look at the Relationship between Sharpness and Generalization](https://mlsanity.com/paper/2302.07011/) (2023)
- [On the Relation Between the Sharpest Directions of DNN Loss and the SGD Step Length](https://mlsanity.com/paper/1807.05031/) (2018)
- [A Walk with SGD](https://mlsanity.com/paper/1802.08770/) (2018)
- [Why Do We Need Weight Decay in Modern Deep Learning?](https://mlsanity.com/paper/2310.04415/) (2023)
- [SGD with Large Step Sizes Learns Sparse Features](https://mlsanity.com/paper/2210.05337/) (2022)
- [Theoretical Analysis of Auto Rate-Tuning by Batch Normalization](https://mlsanity.com/paper/1812.03981/) (2018)

## Built on by (most cited first, 6 of 6)

- [SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMs](https://mlsanity.com/paper/2509.20758/) (2025)
- [Gradient Descent with Large Step Sizes: Chaos and Fractal Convergence Region](https://mlsanity.com/paper/2509.25351/) (2025)
- [SGD as Free Energy Minimization: A Thermodynamic View on Neural Network Training](https://mlsanity.com/paper/2505.23489/) (2025)
- [Fixed Aggregation Features Can Rival GNNs](https://mlsanity.com/paper/2601.19449/) (2026)
- [How does the optimizer implicitly bias the model merging loss landscape?](https://mlsanity.com/paper/2510.04686/) (2025)
- [Can Stationary Distributions of Scale-Invariant Neural Networks Be Described by the Thermodynamics of an Ideal Gas?](https://mlsanity.com/paper/2511.07308/) (2025)

## Abstract (arXiv)

It is generally accepted that starting neural networks training with large learning rates (LRs) improves generalization. Following a line of research devoted to understanding this effect, we conduct an empirical study in a controlled setting focusing on two questions: 1) how large an initial LR is required for obtaining optimal quality, and 2) what are the key differences between models trained with different LRs? We discover that only a narrow range of initial LRs slightly above the convergence threshold lead to optimal results after fine-tuning with a small LR or weight averaging. By studying the local geometry of reached minima, we observe that using LRs from this optimal range allows for the optimization to locate a basin that only contains high-quality minima. Additionally, we show that these initial LRs result in a sparse set of learned features, with a clear focus on those most relevant for the task. In contrast, starting training with too small LRs leads to unstable minima and attempts to learn all features simultaneously, resulting in poor generalization. Conversely, using initial LRs that are too large fails to detect a basin with good solutions and extract meaningful patterns from the data.