  In the rapidly advancing arena of large language models (LLMs), a key
challenge is to enhance their capabilities amid a looming shortage of
high-quality training data. Our study starts from an empirical strategy for the
light continual training of LLMs using their original pre-training data sets,
with a specific focus on selective retention of samples that incur moderately
high losses. These samples are deemed informative and beneficial for model
refinement, contrasting with the highest-loss samples, which would be discarded
due to their correlation with data noise and complexity. We then formalize this
strategy into a principled framework of Instance-Reweighted Distributionally
Robust Optimization (IR-DRO). IR-DRO is designed to dynamically prioritize the
training focus on informative samples through an instance reweighting
mechanism, streamlined by a closed-form solution for straightforward
integration into established training protocols. Through rigorous
experimentation with various models and datasets, our findings indicate that
our sample-targeted methods significantly improve LLM performance across
multiple benchmarks, in both continual pre-training and instruction tuning
scenarios. Our codes are available at
https://github.com/VITA-Group/HardFocusTraining.
