How to Set the Batch Size for Large-Scale Pre-training?

• URL: http://arxiv.org/abs/2601.05034v2
• Date: Fri, 09 Jan 2026 03:25:57 GMT
• Title: How to Set the Batch Size for Large-Scale Pre-training?
• Authors: Yunhua Zhou, Junhao Huang, Shuhao Xing, Yechen Zhang, Runyu Peng, Qiping Guo, Xipeng Qiu,
• Abstract summary: This paper proposes a revised E(S) relationship tailored for the Warmup-Stable-Decay (WSD) learning rate scheduler.<n>Our theoretical analysis reveals two fundamental properties of WSD-based pre-training: 1) B_min, the minimum batch size threshold required to achieve a target loss, and 2) B_opt, the optimal batch size that maximizes data efficiency by minimizing total tokens.
• Score: 46.58311647781476
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The concept of Critical Batch Size, as pioneered by OpenAI, has long served as a foundational principle for large-scale pre-training. However, with the paradigm shift towards the Warmup-Stable-Decay (WSD) learning rate scheduler, we observe that the original theoretical framework and its underlying mechanisms fail to align with new pre-training dynamics. To bridge this gap between theory and practice, this paper derives a revised E(S) relationship tailored for WSD scheduler, characterizing the trade-off between training data consumption E and steps S during pre-training. Our theoretical analysis reveals two fundamental properties of WSD-based pre-training: 1) B_min, the minimum batch size threshold required to achieve a target loss, and 2) B_opt, the optimal batch size that maximizes data efficiency by minimizing total tokens. Building upon these properties, we propose a dynamic Batch Size Scheduler. Extensive experiments demonstrate that our revised formula precisely captures the dynamics of large-scale pre-training, and the resulting scheduling strategy significantly enhances both training efficiency and final model quality.

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