MGUP: A Momentum-Gradient Alignment Update Policy for Stochastic Optimization

• URL: http://arxiv.org/abs/2606.17526v1
• Date: Tue, 16 Jun 2026 05:10:29 GMT
• Title: MGUP: A Momentum-Gradient Alignment Update Policy for Stochastic Optimization
• Abstract summary: We propose textbfMGUP, a novel mechanism for selective updates.<n>textbfMGUP augments standard momentum-based proportions by applying larger step-sizes.<n>textbfMGUP seamlessly integrates with AdamW, Lion, and Muon.
• Score: 21.42805615044331
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Efficient optimization is essential for training large language models. Although intra-layer selective updates have been explored, a general mechanism that enables fine-grained control while ensuring convergence guarantees is still lacking. To bridge this gap, we propose \textbf{MGUP}, a novel mechanism for selective updates. \textbf{MGUP} augments standard momentum-based optimizers by applying larger step-sizes to a selected fixed proportion of parameters in each iteration, while applying smaller, non-zero step-sizes to the rest. As a nearly {plug-and-play} module, \textbf{MGUP} seamlessly integrates with optimizers such as AdamW, Lion, and Muon. This yields powerful variants such as \textbf{MGUP-AdamW}, \textbf{MGUP-Lion}, and \textbf{MGUP-Muon}. Under standard assumptions, we provide theoretical convergence guarantees for \textbf{MGUP-AdamW} (without weight decay) in stochastic optimization. Extensive experiments across diverse tasks, including MAE pretraining, LLM pretraining, and downstream fine-tuning, demonstrate that our \textbf{MGUP}-enhanced optimizers achieve superior or more stable performance compared to their original base optimizers. We offer a principled, versatile, and theoretically grounded strategy for efficient intra-layer selective updates, accelerating and stabilizing the training of large-scale models. The code is publicly available at https://github.com/MaeChd/MGUP.

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