# Don't Decay the Learning Rate, Increase the Batch Size

arXiv: https://arxiv.org/abs/1711.00489 · HTML: https://mlsanity.com/paper/1711.00489/

## Key facts

- Cited by 320 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2017.

## Built on by (most cited first, 30 of 320)

- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [Challenges and Applications of Large Language Models](https://mlsanity.com/paper/2307.10169/) (2023)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Federated Learning with Buffered Asynchronous Aggregation](https://mlsanity.com/paper/2106.06639/) (2021)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations](https://mlsanity.com/paper/2405.18392/) (2024)
- [ExT5: Towards Extreme Multi-Task Scaling for Transfer Learning](https://mlsanity.com/paper/2111.10952/) (2021)
- [Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability](https://mlsanity.com/paper/2209.15594/) (2022)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)
- [End-to-End Speech Recognition: A Survey](https://mlsanity.com/paper/2303.03329/) (2023)
- [Simple-BEV: What Really Matters for Multi-Sensor BEV Perception?](https://mlsanity.com/paper/2206.07959/) (2022)
- [Label Noise SGD Provably Prefers Flat Global Minimizers](https://mlsanity.com/paper/2106.06530/) (2021)
- [Large-Scale Differentially Private BERT](https://mlsanity.com/paper/2108.01624/) (2021)
- [Do We Actually Need Dense Over-Parameterization? In-Time Over-Parameterization in Sparse Training](https://mlsanity.com/paper/2102.02887/) (2021)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [Vision Transformers provably learn spatial structure](https://mlsanity.com/paper/2210.09221/) (2022)
- [Automatic Clipping: Differentially Private Deep Learning Made Easier and Stronger](https://mlsanity.com/paper/2206.07136/) (2022)
- [Zeus: Understanding and Optimizing GPU Energy Consumption of DNN Training](https://mlsanity.com/paper/2208.06102/) (2022)
- [On Large-Cohort Training for Federated Learning](https://mlsanity.com/paper/2106.07820/) (2021)
- [On the Validity of Modeling SGD with Stochastic Differential Equations (SDEs)](https://mlsanity.com/paper/2102.12470/) (2021)
- [How Does Critical Batch Size Scale in Pre-training?](https://mlsanity.com/paper/2410.21676/) (2024)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [AdaptSFL: Adaptive Split Federated Learning in Resource-constrained Edge Networks](https://mlsanity.com/paper/2403.13101/) (2024)
- [Randomness In Neural Network Training: Characterizing The Impact of Tooling](https://mlsanity.com/paper/2106.11872/) (2021)
- [On the Maximum Hessian Eigenvalue and Generalization](https://mlsanity.com/paper/2206.10654/) (2022)
- [Rethinking "Batch" in BatchNorm](https://mlsanity.com/paper/2105.07576/) (2021)

## Abstract (arXiv)

It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate ε and scaling the batch size B propto ε. Finally, one can increase the momentum coefficient m and scale B propto 1/(1-m), although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train ResNet-50 on ImageNet to 76.1% validation accuracy in under 30 minutes.
