Data Uniformity Improves Training Efficiency and More, with a Convergence Framework Beyond the NTK Regime

Data selection plays a crucial role in data-driven decision-making, including in large language models (LLMs), and is typically task-dependent. Properties such as data quality and diversity have been extensively studied and are known to enhance model performance. However, it remains unclear whether there exist other quantitative and general principles of data selection that can consistently improve performance, especially for complex tasks with limited prior knowledge. In this paper, we demonstrate that selecting more uniformly distributed data can improve training efficiency while enhancing performance. Our analysis introduces a convergence framework for GD beyond the Neural Tangent Kernel (NTK) regime, applicable to a broad class of architectures, including transformers, without requiring Lipschitz smoothness. This framework further provides theoretical justification for the use of residual connections and function compositions in deep neural architectures. In the end, we conduct comprehensive experiments for supervised fine-tuning across various settings, including different optimization strategies, model sizes, and training datasets. The results consistently demonstrate that selecting data by maximizing pairwise distance significantly accelerates training and achieves comparable or better performance in LLMs across diverse datasets. The y-axis shows the time (in minutes) required to reach each target loss for the first time. Uniform selection consistently leads to faster convergence, indicating improved training efficiency. Data selection is fundamental to a lot of applications including large language models (LLMs) (Al-balak et al., 2024; Zhao et al., 2023; Chang et al., 2024), such as TeaMs-RL (Gu et al., 2024) and WizardLM (Xu et al., 2024). One main difficulty of data selection is that it is often tailored to specific tasks. Therefore, it is crucial to establish general and applicable rules to guide the data selection process. Existing rules include improving data quality and data diversity (Muennighoff et al., 2025; Albalak et al., 2024; Gu et al., 2024), which have been widely studied and are recognized for their positive impact on model performance.