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

Abstract: Data selection plays a crucial role in data-driven decision-making, including in 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. Specifically, we establish that more uniform (less biased) distribution leads to a larger minimum pairwise distance between data points, denoted by $h_{\min}$, and prove that a smaller $h_{\min}$ can slow down the training dynamics of gradient descent (GD). Moreover, we theoretically show that the approximation error of neural networks decreases as $h_{\min}$ increases. 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. Code and Datasets are available at the link: https://github.com/SafeRL-Lab/data-uniformity.