# Nesterov Method for Asynchronous Pipeline Parallel Optimization

arXiv: https://arxiv.org/abs/2505.01099 · HTML: https://mlsanity.com/paper/2505.01099/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books](https://mlsanity.com/paper/1506.06724/) (2015)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Memory-Efficient Pipeline-Parallel DNN Training](https://mlsanity.com/paper/2006.09503/) (2020)
- [Asynchronous Stochastic Gradient Descent with Delay Compensation](https://mlsanity.com/paper/1609.08326/) (2016)
- [Asynchronous SGD Beats Minibatch SGD Under Arbitrary Delays](https://mlsanity.com/paper/2206.07638/) (2022)
- [SWARM Parallelism: Training Large Models Can Be Surprisingly Communication-Efficient](https://mlsanity.com/paper/2301.11913/) (2023)
- [PipeMare: Asynchronous Pipeline Parallel DNN Training](https://mlsanity.com/paper/1910.05124/) (2019)
- [Towards Crowdsourced Training of Large Neural Networks using Decentralized Mixture-of-Experts](https://mlsanity.com/paper/2002.04013/) (2020)
- [Advances in Asynchronous Parallel and Distributed Optimization](https://mlsanity.com/paper/2006.13838/) (2020)
- [Zero Bubble Pipeline Parallelism](https://mlsanity.com/paper/2401.10241/) (2023)
- [Asynchrony begets Momentum, with an Application to Deep Learning](https://mlsanity.com/paper/1605.09774/) (2016)
- [Efficient and Robust Parallel DNN Training through Model Parallelism on Multi-GPU Platform](https://mlsanity.com/paper/1809.02839/) (2018)
- [Asynchronous Local-SGD Training for Language Modeling](https://mlsanity.com/paper/2401.09135/) (2024)
- [XPipe: Efficient Pipeline Model Parallelism for Multi-GPU DNN Training](https://mlsanity.com/paper/1911.04610/) (2019)
- [Gap Aware Mitigation of Gradient Staleness](https://mlsanity.com/paper/1909.10802/) (2019)
- [Taming Momentum in a Distributed Asynchronous Environment](https://mlsanity.com/paper/1907.11612/) (2019)

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

- [AsyncMesh: Fully Asynchronous Optimization for Data and Pipeline Parallelism](https://mlsanity.com/paper/2601.22442/) (2026)
- [Mitigating Staleness in Asynchronous Pipeline Parallelism via Basis Rotation](https://mlsanity.com/paper/2602.03515/) (2026)
- [AMDP: Asynchronous Multi-Directional Pipeline Parallelism for Large-Scale Models Training](https://mlsanity.com/paper/2605.29664/) (2026)
- [Unextractable Protocol Models: Collaborative Training and Inference without Weight Materialization](https://mlsanity.com/paper/2605.23464/) (2026)
- [Breaking the Bubble: Asynchronous Pipeline Parallel Training with Bounded Weight Inconsistency](https://mlsanity.com/paper/2606.07881/) (2026)
- [One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining](https://mlsanity.com/paper/2606.30634/) (2026)

## Abstract (arXiv)

Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100% pipeline utilization by construction. However, it is inherently challenging as the weights and gradients are no longer synchronized, leading to stale (or delayed) gradients. To alleviate this, we introduce a variant of Nesterov Accelerated Gradient (NAG) for asynchronous optimization in PP. Specifically, we modify the look-ahead step in NAG to effectively address the staleness in gradients. We theoretically prove that our approach converges at a sublinear rate in the presence of fixed delay in gradients. Our experiments on large-scale language modelling tasks using decoder-only architectures with up to 1B parameters, demonstrate that our approach significantly outperforms existing asynchronous methods, even surpassing the synchronous baseline.