# Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models

arXiv: https://arxiv.org/abs/2208.06677 · HTML: https://mlsanity.com/paper/2208.06677/

## Key facts

- Cited by 174 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 121 references that are in the map.
- First posted on arXiv 13 Aug 2022.

## Builds on (most cited first, 30 of 68)

- [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)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)

## Built on by (most cited first, 30 of 174)

- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (2024)
- [EDGE: Editable Dance Generation From Music](https://mlsanity.com/paper/2211.10658/) (2022)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)
- [LHRS-Bot: Empowering Remote Sensing with VGI-Enhanced Large Multimodal Language Model](https://mlsanity.com/paper/2402.02544/) (2024)
- [Tamper-Resistant Safeguards for Open-Weight LLMs](https://mlsanity.com/paper/2408.00761/) (2024)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [Muon Optimizes Under Spectral Norm Constraints](https://mlsanity.com/paper/2506.15054/) (2025)
- [MARS: Unleashing the Power of Variance Reduction for Training Large Models](https://mlsanity.com/paper/2411.10438/) (2024)
- [Lodge: A Coarse to Fine Diffusion Network for Long Dance Generation Guided by the Characteristic Dance Primitives](https://mlsanity.com/paper/2403.10518/) (2024)
- [Consistent3D: Towards Consistent High-Fidelity Text-to-3D Generation with Deterministic Sampling Prior](https://mlsanity.com/paper/2401.09050/) (2024)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [The Ninth NTIRE 2024 Efficient Super-Resolution Challenge Report](https://mlsanity.com/paper/2404.10343/) (2024)
- [Friendly Sharpness-Aware Minimization](https://mlsanity.com/paper/2403.12350/) (2024)
- [PLIP: Language-Image Pre-training for Person Representation Learning](https://mlsanity.com/paper/2305.08386/) (2023)
- [CMID: A Unified Self-Supervised Learning Framework for Remote Sensing Image Understanding](https://mlsanity.com/paper/2304.09670/) (2023)
- [Cautious Optimizers: Improving Training with One Line of Code](https://mlsanity.com/paper/2411.16085/) (2024)
- [Understanding Imbalanced Semantic Segmentation Through Neural Collapse](https://mlsanity.com/paper/2301.01100/) (2023)
- [DNeRV: Modeling Inherent Dynamics via Difference Neural Representation for Videos](https://mlsanity.com/paper/2304.06544/) (2023)
- [Ditto: Motion-Space Diffusion for Controllable Realtime Talking Head Synthesis](https://mlsanity.com/paper/2411.19509/) (2024)
- [Compute-Efficient Deep Learning: Algorithmic Trends and Opportunities](https://mlsanity.com/paper/2210.06640/) (2022)
- [Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity](https://mlsanity.com/paper/2310.17998/) (2023)
- [LDAdam: Adaptive Optimization from Low-Dimensional Gradient Statistics](https://mlsanity.com/paper/2410.16103/) (2024)
- [Co-Speech Gesture Video Generation via Motion-Decoupled Diffusion Model](https://mlsanity.com/paper/2404.01862/) (2024)
- [Implicit Bias and Fast Convergence Rates for Self-attention](https://mlsanity.com/paper/2402.05738/) (2024)
- [On the Convergence of Muon and Beyond](https://mlsanity.com/paper/2509.15816/) (2025)
- [The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training](https://mlsanity.com/paper/2502.19002/) (2025)
- [Boosting Neural Representations for Videos with a Conditional Decoder](https://mlsanity.com/paper/2402.18152/) (2024)
- [On Efficient Training of Large-Scale Deep Learning Models: A Literature Review](https://mlsanity.com/paper/2304.03589/) (2023)

## Abstract (arXiv)

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model training speed across deep networks, we propose the ADAptive Nesterov momentum algorithm, Adan for short. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra overhead of computing gradient at the extrapolation point. Then, Adan adopts NME to estimate the gradient's first- and second-order moments in adaptive gradient algorithms for convergence acceleration. Besides, we prove that Adan finds an ε-approximate first-order stationary point within O(ε-3.5) stochastic gradient complexity on the non-convex stochastic problems (e.g., deep learning problems), matching the best-known lower bound. Extensive experimental results show that Adan consistently surpasses the corresponding SoTA optimizers on vision, language, and RL tasks and sets new SoTAs for many popular networks and frameworks, e.g., ResNet, ConvNext, ViT, Swin, MAE, DETR, GPT-2, Transformer-XL, and BERT. More surprisingly, Adan can use half of the training cost (epochs) of SoTA optimizers to achieve higher or comparable performance on ViT, GPT-2, MAE, etc., and also shows great tolerance to a large range of minibatch size, e.g., from 1k to 32k. Code is released at https://github.com/sail-sg/Adan, and has been used in multiple popular deep learning frameworks or projects.