Data Pruning and Neural Scaling Laws: Fundamental Limitations of Score-Based Algorithms

Abstract

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results (Guo, B. Zhao, and Bai, 2022) reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of 30% or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; see (Sorscher et al., 2022), where the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate “No Free Lunch" theorems for data pruning and discuss potential solutions to these limitations.