Quantitative Analysis of the Relationship Between Optimal Learning Rate and Batch Size Scaling in Large Language Models

The rapid development of natural language processing has led to the emergence of sophisticated models capable of performing a wide array of tasks with human-like proficiency. Identifying the optimal relationship between learning rate and batch size is crucial for enhancing the efficiency and effectiveness of training these models. Through systematic experimentation with models such as Baidu Ernie, Meta Llama, and Moonshot Kimi, this research demonstrates a linear relationship between these hyperparameters, providing a practical framework for their adjustment. Results indicate that appropriate scaling of learning rates with batch sizes can significantly improve training efficiency, model accuracy, and convergence time. The findings offer valuable insights into the dynamics of model training, presenting a scalable approach that can reduce computational costs and enhance model robustness, thereby contributing to the broader field of artificial intelligence.