  Despite the effectiveness of data selection for large language models (LLMs)
during pretraining and instruction fine-tuning phases, improving data
efficiency in supervised fine-tuning (SFT) for specialized domains poses
significant challenges due to the complexity of fine-tuning data. To bridge
this gap, we introduce an effective and scalable data selection method for SFT,
SmallToLarge (S2L), which leverages training trajectories from small models to
guide the data selection for larger models. We demonstrate through extensive
experiments that S2L significantly improves data efficiency in SFT for
mathematical problem-solving, reducing the training data to just 11% of the
original MathInstruct dataset (Yue et al., 2023) to match full dataset
performance while outperforming state-of-the-art data selection algorithms by
an average of 4.7% across 6 in- and out-domain evaluation datasets. Remarkably,
selecting only 50K data for SFT, S2L achieves a 32.7% accuracy on the most
challenging MATH (Hendrycks et al., 2021) benchmark, improving Phi-2 (Li et
al., 2023b) by 16.6%. In clinical text summarization on the MIMIC-III dataset
(Johnson et al., 2016), S2L again outperforms training on the full dataset
using only 50% of the data. Notably, S2L can perform data selection using a
reference model 40x smaller than the target model, proportionally reducing the
cost of data selection.
